Physics Ray Optics Chapter 9 PYQs PDF (CBSE)

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A-PDF Watermark DEMO: Purchase from www.A-PDF.com to remove the watermark www.cbse.page www.cbse.page * Unit VI Optics www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page ’ Chapter 9 ™ Ray Optics and Optical Instruments www.cbse.page www.cbse.page  Weightage for CBSE Board 2024 Unit V and VI À Chapters Combined www.cbse.page 2 Chapter 8 www.cbse.page Weightage is 2 Chapter 9 18 Marks 2 Chapter 10 It’s not fixed which chapters will have more weightage, but overall weightage will be 18 Marks. It may vary too in your question www.cbse.page www.cbse.page paper. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page ` Syllabus Reflection of light, spherical mirrors, mirror formula, refraction of light, total internal reflection and optical fibers, refraction at spherical surfaces, lenses, thin lens formula, lens maker’s formula, magnification, power of a lens, www.cbse.page www.cbse.page combination of thin lenses in contact, refraction of light through a prism. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page Strict Advice www.cbse.page www.cbse.page It’s a deep request, please practice at least all total 16 question papers (paper code given below) of 2023 and 2024 to score good marks in your 2025 board exam, even you have not prepared well for your board exam; www.cbse.page www.cbse.page ¥ 2024 July 55/S/1 All Sets ¥ 2024 July 55(B)/S ¥ 2024 March 55/1 All Sets ¥ 2024 March 55/2 All Sets ¥ 2024 March 55/3 www.cbse.page All Sets www.cbse.page ¥ 2024 March 55/4 All Sets ¥ 2024 March 55/5 All Sets ¥ 2024 March 55(B) ¥ 2023 July 55/C All Sets ¥ 2023 July 55(B)/C ¥ 2023 March 55/1 All Sets www.cbse.page www.cbse.page ¥ 2023 March 55/2 All Sets ¥ 2023 March 55/3 All Sets ¥ 2023 March 55/4 All Sets ¥ 2023 March 55/5 All Sets ¥ 2023 March 55(B) www.cbse.page www.cbse.page Many questions which were www.cbse.page www.cbse.page not according to cbse 2025 syllabus or out of syllabus, from year 2019 to 2022 has www.cbse.page www.cbse.page been excluded. Because it created too much confusion to students www.cbse.page www.cbse.page Be aware, that, 2019 to 2022 had different syllabus. You will find only those questions which is www.cbse.page www.cbse.page according to cbse 2025 syllabus www.cbse.page www.cbse.page www.cbse.page www.cbse.page = Chapter 9 www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ¢ 2024 PYQs www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2024 July ¥ 55/S/1 All Sets www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 1 ¥ 55/S, Set 1 A point object is placed in air at a distance of 4R on the principal axis of a convex spherical surface of radius of curvature R separating two mediums, air and glass. As the object is moved towards the www.cbse.page www.cbse.page surface, the image formed is : (a) always real (b) always virtual (c) first virtual and then real (d) first real and then virtual www.cbse.page www.cbse.page Answer A 1 Marks (d) first real and then virtual š 2024 PYQ 2 ¥ 55/S, Set 1 www.cbse.page www.cbse.page Assertion (A) : Although the surfaces of a goggle lens are curved, it does not have any power. Reason (R) : In case of goggles, both the curved surfaces are curved on the same side and have equal radii of curvature. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation www.cbse.page www.cbse.page of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Both Assertion (A) and Reason (R) are false. Answer A 1 Marks www.cbse.page www.cbse.page (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). š 2024 PYQ 3 ¥ 55/S, Set 1 A point light source rests on the bottom of a www.cbse.page www.cbse.page bucket filled with a liquid of refractive index µ = 1.25 up to height of 10 cm. Calculate : (a) the critical angle for liquid−air interface (b) radius of circular light patch formed on the www.cbse.page www.cbse.page  www.cbse.page www.cbse.page surface by light emerging from the source. Answer A 2 Marks 1 (a) sin i c = µ µ ¶ 4 5 ∵ µ = 1.25 = www.cbse.page www.cbse.page sin i c = 5 4 µ ¶ −1 4 ic = sin 5 OR ◦ i c = 53 r www.cbse.page www.cbse.page (b) sin i c = p 2 r +h 2 2 µ ¶ 2 r 4 2 2 = r +h 5 2 2 2 25r = 16r + 16h www.cbse.page www.cbse.page 2 9r = 1600 40 r= cm 3 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 4 ¥ 55/S, Set 1 (i) What are the two main considerations for designing the objective and eyepiece lenses of an astronomical telescope ? Obtain the expression for magnifying power of the www.cbse.page www.cbse.page telescope when the final image is formed at infinity. ◦ (ii) A ray of light is incident at an angle of 45 at one face of an equilateral triangular prism and passes symmetrically through the prism. www.cbse.page www.cbse.page Calculate : (1) the angle of deviation produced by the prism (2) the refractive index of the material of the prism www.cbse.page OR www.cbse.page (i) Describe a simple activity to observe diffraction pattern due to a single slit. (ii) The figure below shows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle www.cbse.page www.cbse.page  www.cbse.page www.cbse.page with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. When the liquid is removed and the experiment is repeated, the new distance is www.cbse.page www.cbse.page 30.0 cm. Find the refractive index of the liquid. www.cbse.page www.cbse.page Answerwww.cbse.page A 5 Marks www.cbse.page Two main considerations Objective should have 1. Larger diameter 2. Larger focal length www.cbse.page www.cbse.page  www.cbse.page www.cbse.page Eye piece should have 1. Smaller diameter 2. Smaller focal length www.cbse.page www.cbse.page www.cbse.page www.cbse.page Magnifying power of telescope Magnifying power is the ratio of the angle β subtended at the eye by the final images to the angle α which the object subtends at the lens or www.cbse.page www.cbse.page eye β h f0 f0 m≈ ≈ · = α fe h fe (ii) i + e = D + A at D = Dm, i = e www.cbse.page www.cbse.page  2i = Dm + A www.cbse.page www.cbse.page ◦ 2 × 45 = Dm + 60 ◦ Dm = 30 µ ¶ A + Dm sin 2 µ= µ ¶ www.cbse.page www.cbse.page A sin 2 µ ◦ ◦ ¶ 60 + 30 sin p 2 µ= µ ◦¶ = 2 60 sin 2 www.cbse.page www.cbse.page OR (i) We hold two razor blades in such a way that their edges are parallel and with a narrow slit in between. Keep the slit parallel to the filament of electric bulb, right in front of the www.cbse.page www.cbse.page eye. A diffraction is seen with its bright and dark bands. · ¸ 1 1 1 (ii) = (µ − 1) − f R1 R2 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page Focal length of convex lens, f 1 = 30 cm · ¸ 1 1 1 = (1.5 − 1) − 30 R (−R) R = 30 cm focal length of combination, f = 45 cm focal length of plane concave lens of liquid. www.cbse.page www.cbse.page 1 1 1 = − f2 f f1 1 1 1 = − f 2 45 30 f 2 = −90 cm Using lens maker’s formula www.cbse.page www.cbse.page · ¸ 1 ¡ ¢ 1 1 = µl − 1 − −90 −30 ∞ 4 µl = 3 š 2024 PYQ 5 www.cbse.page ¥ 55/S, Set 3 www.cbse.page (a) Draw the shape of intensity distribution curve of the fringes due to diffraction at a single slit. (b) Derive the relation for the power of combination of two lenses placed in contact www.cbse.page www.cbse.page  www.cbse.page www.cbse.page co−axially. Answer A 3 Marks (a) www.cbse.page www.cbse.page www.cbse.page www.cbse.page (b) www.cbse.page www.cbse.page For the image formed by first lens A, we get www.cbse.page www.cbse.page  1 1 1 www.cbse.page www.cbse.page − =.....(1) v1 u f 1 For the image formed by the second lens B , we get 1 1 1 − =.....(2) v v1 f 2 Adding eqs (1) and (2) we get www.cbse.page www.cbse.page 1 1 1 1 − = +.....(3) v u f1 f2 If the two lens system is regarded as equivalent to a single lens of focal length f , we have 1 1 1 − =.....(4) v u f www.cbse.page www.cbse.page From eqs (3) & (4) 1 1 1 = + f f1 f2 1 As, P = f www.cbse.page www.cbse.page Hence, P = P 1 + P 2 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2024 July ¥ 55(B)/S All Sets www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 6 ¥ 55(B) / S, Set 5 Assertion (A) : In optical fibres, the refractive index of cladding must be lesser than that of the core. Reason (R) : Total internal reflection takes place www.cbse.page www.cbse.page only when the ray passes from denser to rarer medium. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the www.cbse.page www.cbse.page Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true but Reason (R) is false. www.cbse.page www.cbse.page (d) Assertion (A) is false and Reason (R) is also false. Answer A 1 Marks (a) Both Assertion (A) and Reason (R) are true and www.cbse.page www.cbse.page  www.cbse.page www.cbse.page Reason (R) is the correct explanation of the Assertion (A). š 2024 PYQ 7 ¥ 55(B) / S, Set 5 Why does a water tank appear shallow ? Explain. Write the relation between real depth and www.cbse.page www.cbse.page apparent depth of the tank with the refractive index of water. OR What are optical fibres ? How does a light ray travel through an optical fibre ? Give two www.cbse.page www.cbse.page applications of optical fibres. Answer A 2 Marks It is due to refraction of light. Light coming out of the water surface deviates away from normal and www.cbse.page www.cbse.page as a result appear to come from a point above the bottom of water tank. Relation between real depth, apparent depth and refractive index of water. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page Real depth Refractive index = Apparent depth Rd Alternatively−µw = Ad OR Optical fibres are composite glass/quartz fibres www.cbse.page www.cbse.page consisting of a core & a cladding used to transmit audio and video signals through long distances. When a signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflections along the length www.cbse.page www.cbse.page of the fibre and finally comes out at the other end. Two applications of optical fibres (1) For communication (2) For decorative purpose (3) For examining internal organs www.cbse.page www.cbse.page š 2024 PYQ 8 ¥ 55(B) / S, Set 5 A glass biconvex lens of focal length 0.6 m and refractive index 1.5 is immersed in a medium of refractive index 2.0. Find the new power of the www.cbse.page www.cbse.page  www.cbse.page www.cbse.page lens and the nature of lens. Answer A 3 Marks According to Lens−Makers formula : µ ¶ 1 1 1 = (µ − 1) − f www.cbse.page R1 R2 www.cbse.page For biconvex lens µ ¶ 1 1 1 = (1.5 − 1) − − − − − − −(1) 0.6 R1 R2 When immersed µ in medium ¶µ ¶: − 1 1.5 1 1 = −1 − − − − − − −(2) f 2 www.cbse.page R1 R2 www.cbse.page On solving equation (1) and (2) : − 1 5 =− m f 6 5 P =− D 6 Nature of lens will be concave or diverging. www.cbse.page www.cbse.page š 2024 PYQ 9 ¥ 55(B) / S, Set 5 (i) Write the relation between u, vand R for a convex spherical surface when refraction takes place from optically rarer to denser www.cbse.page www.cbse.page  www.cbse.page www.cbse.page medium. Using it, derive ‘lens maker formula’ for a double convex lens. (ii) Two thin lenses of power +25 D and –5 D are kept in contact with each other. (1) Calculate the focal length of the combination. www.cbse.page www.cbse.page (2) An object of 4 cm height is placed at a distance of 25 cm from this combination. What is the position and size of the image formed ? Answer A 5 Marks www.cbse.page www.cbse.page (i) For a convex spherical surface, for light going from optically rarer to optically denser medium n1 n2 n2 − n1 + = −u v R For the refraction through the first convex www.cbse.page www.cbse.page surface (light going from rarer to denser medium), the relation will be n1 n2 n2 − n1 + =.....(1) −u v1 R1 For the refraction through the second convex www.cbse.page www.cbse.page  www.cbse.page www.cbse.page surface (light going from denser to rarer medium), the relation will be −n2 n1 n1 − n2 + =.....(2) v1 v R2 Adding equation (1) and (2) µ ¶ n1 n1 www.cbse.page 1 1 www.cbse.page − = (n2 − n1) −.....(3) v u R1 R2 From lens formula 1 1 1 = − f v u Using equation (3) and (4) µ www.cbse.page ¶ www.cbse.page 1 1 1 = (n21 − 1) − f R1 R2 (ii) (1) P1 = +25D ⇒ f1 = 4 cm P2 = −5D ⇒ f2 = −20 cm f1f2 4 × (−20) f= = f1 + f2 www.cbse.page −16 www.cbse.page f = 5 cm (2) From lens formula 1 1 1 − = v u f www.cbse.page www.cbse.page 1 5−1 www.cbse.page www.cbse.page = v 25 on solving 25 v= cm 4 I v Magnification m = = www.cbse.page www.cbse.page O u v 25 I = ×O = ×4 u 4 × (−25) I = −1 cm www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2024 March ¥ 55/5 All Sets www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 10 ¥ 55/5, Set 1 The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm, the magnification obtained by the www.cbse.page www.cbse.page microscope for most suitable viewing by relaxed eye is : (a) 250 (b) 200 (c) 150 (d) 125 Answer www.cbse.page A 1 Marks www.cbse.page (d) 125 š 2024 PYQ 11 ¥ 55/5, Set 1 A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. www.cbse.page www.cbse.page Calculate its magnifying power in normal adjustment and the distance of the image formed by the objective. Answer A 2 Marks www.cbse.page www.cbse.page  www.cbse.page www.cbse.page f 0 150 |m| = = = 30 fe 5 1 1 1 = − f v u 1 1 1 = − 150 v ∞ www.cbse.page www.cbse.page v = 150 cm š 2024 PYQ 12 ¥ 55/5, Set 1 Case Based Question A prism is an optical medium bounded by three www.cbse.page www.cbse.page refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by www.cbse.page µ ¶. www.cbse.page A + δm A µ = sin sin 2 2 If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and www.cbse.page www.cbse.page  www.cbse.page www.cbse.page is totally internally reflected. (i) The critical angle for glass is θ1 and that for water is θ2. The critical angle for glass-water surface would be (given a µg = 1.5, a µw = 1.33) www.cbse.page www.cbse.page (a) less than θ2 (b) between θ1 and θ2 (c) greater than θ2 (d) less than θ1 www.cbse.page www.cbse.page (ii) When a ray of light of wavelength λ and frequency v is refracted into a denser medium (a) λ and v both increase. (b) λ increases but v is unchanged. (c) λ decreases but v is unchanged. www.cbse.page www.cbse.page (d) λ and v both decrease. (iii) The critical angle for a ray of light passing from glass to water is minimum for (a) red colour (b) blue colour www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (c) yellow colour (d) violet colour OR (iii) Three beams of red, yellow and violet colours are passed through a prism, one by one under the same condition. When the prism is in the www.cbse.page www.cbse.page position of minimum deviation, the angles of refraction from the second surface are r R , r Y and r V respectively. Then (a) r V < r Y < r R (b) r Y < r R < r V (c) r R < r Y < r V www.cbse.page (d) r R = r Y = r V www.cbse.page (iv) A ray of light is incident normally on a prism p ABC of refractive index 2, as shown in figure. After it strikes face AC, it will www.cbse.page www.cbse.page (a) go straight undeviated www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (b) just graze along the face AC (c) refract and go out of the prism (d) undergo total internal reflection Answer A 4 Marks www.cbse.page www.cbse.page (i) (c) greater than θ2 (ii) (c) λ decreases but v is unchanged (iii) (d) violet colour OR (iii) (c) r R < r Y < r V www.cbse.page www.cbse.page (iv) (d) undergo total internal reflection š 2024 PYQ 13 ¥ 55/5, Set 1 An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an www.cbse.page www.cbse.page enlarged image. Answer A 2 Marks www.cbse.page www.cbse.page  www.cbse.page www.cbse.page 1 1 1 = + f v u uf v= u−f Following new cartesian sign conversion www.cbse.page (−u)(− f ) www.cbse.page v= −u − (− f ) uf v= as f > u f −u v is +ve, So image is virtual. v f m=− = > 1 i.e. Enlarged image www.cbse.page www.cbse.page u f −u š 2024 PYQ 14 ¥ 55/5, Set 2 The radius of curvature of a convex mirror is 30 cm. It forms an image of an object which is half the size of the object. Find the separation between www.cbse.page www.cbse.page the object and the image. Answer A 2 Marks v hI 1 m=− = = u ho 2 www.cbse.page www.cbse.page u = −2v www.cbse.page www.cbse.page 1 1 1 = + f v u 1 1 1 = − 15 v 2v On solving www.cbse.page www.cbse.page |v| = 7.5 cm |u| = +15.0 cm Separation = 15.0 + 7.5 = 22.5 cm š 2024 PYQ 15 www.cbse.page ¥ 55/5, Set 3 www.cbse.page A point object is kept 60 cm in front of a spherical convex surface (n = 1.5, radius of curvature 40 cm) The image formed is (a) real, at a distance 1.8 m from the surface. (b) virtual, at a distance 1.8 m from the surface. www.cbse.page www.cbse.page (c) real, at a distance 3.6 m from the surface. (d) virtual, at a distance 3.6 m from the surface. Answer A 1 Marks www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (d) virtual, at a distance 3.6 m from the surface. www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 16 ¥ 55/5, Set 3 A thin converging lens of focal length 10 cm is placed coaxially in contact with a thin diverging lens of focal length 15 cm. How will the combination behave ? Justify your answer. www.cbse.page www.cbse.page Answer A 2 Marks It will behave like a conversing lens. Power of converging lens is more than the power of diverging lens. Hence the combination will www.cbse.page www.cbse.page behave like a conversing lens. Alternatively 100 100 P = P1 + P2 = + 10 −15 10 P= D 3 www.cbse.page www.cbse.page Alternatively 1 1 1 1 1 = + = − f f1 f2 10 15 1 1 ¯ ¯ = ¯ f = 30 cm f 30 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2024 March ¥ 55/4 All Sets www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 17 ¥ 55/4, Set 1 A ray of light is incident normally on one face of an equilateral glass prism of refractive index µ. When the prism is completely immersed in a transparent medium, it is observed that the emergent ray just www.cbse.page www.cbse.page grazes the adjacent face. Find the refractive index of the medium. Answer A 2 Marks www.cbse.page www.cbse.page www.cbse.page www.cbse.page From snell’s law, µ · sin i = µm · sin r ◦ ◦ µ · sin 60 = µm · sin 90 p 3 µm = µ · www.cbse.page 2 www.cbse.page  www.cbse.page www.cbse.page Alternatively 1 µ= sinC µ 1 = ◦ µm sin 60 p 3 µm = µ www.cbse.page www.cbse.page 2 š 2024 PYQ 18 ¥ 55/4, Set 1 An air bubble is trapped at point B (CB = 20 cm) in a glass sphere of radius 40 cm and refractive index www.cbse.page www.cbse.page 1.5 as shown in figure. Find the nature and position of the image of the bubble as seen by an observer at point P. www.cbse.page www.cbse.page www.cbse.page www.cbse.page  OR www.cbse.page www.cbse.page In normal adjustment, for a refracting telescope, the distance between objective and eye piece lens is 1.00 m. If the magnifying power of the telescope is 19 , find the focal length of the objective and the www.cbse.page www.cbse.page eyepiece lens. Answer A 2 Marks Using refraction formula at spherical surface from denser to rarer medium www.cbse.page www.cbse.page n 1 = refractive index of rarer medium n 2 = refractive index of denser medium n1 n2 n1 − n2 − = v u R u = −20 cm, R = −40 cm, n 1 = 1, n 2 = 1.5 www.cbse.page www.cbse.page 1 1.5 1 − 1.5 − = v (−20) (−40) v = −16 cm Nature of image is virtual. www.cbse.page www.cbse.page  OR www.cbse.page www.cbse.page Distance between objective and eyepiece fo + fe = 1.00 m = 100 cm Magnifying power fo |m| = www.cbse.page = 19 2 www.cbse.page fe On solving fo = 95 cm = 0.95 m fe = 5 cm = 0.05 m š 2024 PYQ 19 www.cbse.page ¥ 55/4, Set 1 www.cbse.page Case Study Based Question A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Applying the formula of image formation by a single spherical surface www.cbse.page www.cbse.page successively at the two surfaces of a thin lens, a formula known as lens maker’s formula and hence the basic lens formula can be obtained. The focal length (or power) of a lens depends on the radii of its surfaces and the refractive index of its material www.cbse.page www.cbse.page  www.cbse.page www.cbse.page with respect to the surrounding medium. The refractive index of a material depends on the wavelength of light used. Combination of lenses helps us to obtain diverging or converging lenses of desired power and magnification. www.cbse.page www.cbse.page (i) A thin converging lens of focal length 20 cm and a thin diverging lens of focal length 15 cm are placed coaxially in contact. The power of the combination is −5 −5 4 3 (A) D (B) www.cbse.pageD (C) D (D) D www.cbse.page 6 3 3 2 (ii) The radii of curvature of two surfaces of a convex lensµ are¶ R and 2R. If the focal length of 4 this lens is R, the refractive index of the 3 material of the lens is : www.cbse.page www.cbse.page 5 4 3 7 (A) (B) (C) (D) 3 3 2 5 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (iii) The focal length of an equiconvex lens (a) increases when the lens is dipped in water. (b) increases when the wavelength of incident light decreases. www.cbse.page www.cbse.page (c) increases with decrease in radius of curvature of its surface. (d) decreases when the lens is cut into two identical parts along its principal axis. (iv) A thin convex lens L of focal length 10 cm and www.cbse.page www.cbse.page a concave mirror M of focal length 15 cm are placed coaxially 40 cm apart as shown in figure. A beam of light coming parallel to the principal axis is incident on the lens. www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page The final image will be formed at a distance of (A) 10 cm, left of lens (B) 10 cm, right of lens (C) 20 cm, left of lens (D) 20 cm, right of lens www.cbse.page www.cbse.page OR A beam of light coming parallel to the principal axis of a convex lens L 1 of focal length 16 cm is incident on it. Another convex lens L 2 of focal length 12 cm is placed coaxially www.cbse.page www.cbse.page at a distance 40 cm from L 1. The nature and distance of the final image from L 2 will be (A) real, 24 cm (B) virtual, 12 cm www.cbse.page www.cbse.page (C) real, 32 cm (D) virtual, 18 cm Answer A 4 Marks −5 (i) (B) D 3 www.cbse.page www.cbse.page  3 www.cbse.page www.cbse.page (ii) (C) 2 (iii) (A) increases when a lens is dipped in water. (iv) (B) 10 cm, right from lens. OR www.cbse.page www.cbse.page (A) real, 24 cm š 2024 PYQ 20 ¥ 55/4, Set 1 (i) Draw a ray diagram for the formation of the image of an object by a convex mirror. Hence, obtain the mirror equation. www.cbse.page www.cbse.page (ii) Why are multi-component lenses used for both the objective and the eyepiece in optical instruments? (iii) The magnification of a small object produced by a compound microscope is 200. The focal www.cbse.page www.cbse.page length of the eyepiece is 2 cm and the final image is formed at infinity. Find the magnification produced by the objective. Answerwww.cbse.page A 5 Marks www.cbse.page (i) www.cbse.page www.cbse.page www.cbse.page www.cbse.page For paraxial rays MP can be considered to be a straight line perpendicular to C P , Therefore right ′ ′ angled triangles A B F and MPF are similar www.cbse.page www.cbse.page ′ ′ ′ BA BF = PM FP ′ ′ ′ BA BF Or = (∵ P M = AB ) ——–(1) BA FP www.cbse.page www.cbse.page Since ∠ AP B = ∠ A P B , ′ ′ ′ ′ the right angled triangles A P B and AB P are also similar ′ ′ ′ BA BP Therefore, = ———(2) B A′ B P www.cbse.page www.cbse.page  www.cbse.page www.cbse.page Comparing eq (1) and (2), we get ′ ′ BF BP = 2 FP BP ′ ′ PF −PB B P = www.cbse.page FP BP www.cbse.page Using sign convention ′ P F = f , P B = +v, P B = −u 1 1 1 on solving + = v u f (ii) To improve image quality by minimizing www.cbse.page www.cbse.page various optical aberrations in lenses. (iii) Magnification produced by compound microscope m = mo × me www.cbse.page www.cbse.page m m mo = =¯ ¯ m e ¯¯ D ¯¯ ¯ fe ¯ 200 mo = = 16 25 2 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2024 March ¥ 55/3 All Sets www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 21 ¥ 55/3, Set 1 Assertion (A) : A convex lens, when immersed in a liquid, disappears. Reason (R) : The refractive indices of material of the lens and the liquid are equal. www.cbse.page www.cbse.page (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both Assertion (A) and Reason (R) are true, www.cbse.page www.cbse.page but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Both Assertion (A) and Reason (R) are false. Answer A 1 Marks www.cbse.page www.cbse.page (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion(A). www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 22 ¥ 55/3, Set 1 The magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens. www.cbse.page www.cbse.page Answer A 2 Marks Magnifying power = 24, Distance between lenses =150 cm www.cbse.page fo www.cbse.page = 24 fe f o + f e = 150 cm f e = 6 cm f o = 144 cm www.cbse.page www.cbse.page š 2024 PYQ 23 ¥ 55/3, Set 1 Explain the following : (a) For a simple microscope, the angular size of the object equals the angular size of the image. Yet it offers magnification. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (b) Both plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Answer A 2 Marks (a) Yes, it offers magnification. www.cbse.page www.cbse.page We can keep the small object much closer to the eye than 25 cm and hence have it subtend a large angle. (b) Yes, www.cbse.page www.cbse.page Rays converging to a point behind a plane or convex mirror are reflected to a point in front of the mirror on a screen www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 24 ¥ 55/3, Set 1 (i) Trace the path of a ray of light showing refraction through a triangular prism and hence obtain an expression for angle of deviation ( δ ) in terms of A, i and e, where symbols have their usual www.cbse.page www.cbse.page meanings. Draw a graph showing the variation of angle of deviation with the angle of incidence. (ii) In the figure, a ray of light is incident on a transparent liquid contained in a thin glass box at ◦ an angle of 45 with its one face. The emergent ray www.cbse.page www.cbse.page passes along the face AB. Find the refractive index of the liquid. www.cbse.page www.cbse.page Answer www.cbse.page A 5 Marks www.cbse.page (i) www.cbse.page www.cbse.page www.cbse.page www.cbse.page For quadrilateral AQNR, ∠ A + ∠QN R = 180 ◦......(i ) www.cbse.page www.cbse.page For triangle QNR r 1 + r 2 + ∠QN R = 180 ◦......(i i ) comparing equation (i) and (ii) r 1 + r 2 = A......(i i i ) The angle of deviation www.cbse.page www.cbse.page δ = (i − r 1) + (e − r 2)......(i v) from equation (iii) and (iv) δ = i +e − A www.cbse.page www.cbse.page  www.cbse.page www.cbse.page Graph www.cbse.page www.cbse.page (ii) www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◦ sin 45 =µ sin θ 1 p = µ sin θ www.cbse.page 2 www.cbse.page  www.cbse.page www.cbse.page For second surface, ◦ sin (90 − θ) 1 ◦ = sin 90 µ 1 cos θ p =1 2 sin θ 1 www.cbse.page tan θ = p www.cbse.page 2 From the triangle GEF 1 sin θ = p r 3 3 µ= 2 www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2024 March ¥ 55/2 All Sets www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 25 ¥ 55/2, Set 1 Assertion (A) : The magnifying power of a compound microscope is negative. Reason (R) : The final image formed is erect with respect to the object. www.cbse.page www.cbse.page (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but www.cbse.page www.cbse.page Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false and Reason (R) is also false. www.cbse.page www.cbse.page Answer A 1 Marks (c) Assertion (A) is true, but Reason (R) is false www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 26 ¥ 55/2, Set 1 A convex lens (n = 1·52) has a focal length of 15·0 cm in air. Find its focal length when it is immersed in liquid of refractive index 1·65. What will be the nature of the lens ? www.cbse.page www.cbse.page Answer A 2 Marks For convex lens in air µ ¶µ ¶ 1 ng 1 1 = −1 − fa na R1 R2 For convex lens in liquid www.cbse.page www.cbse.page µ ¶µ ¶ 1 ng 1 1 = −1 − fl nl R1 R2 1.52 − 1 fl 1 = = −6.6 f a 1.52 − 1.65 www.cbse.page www.cbse.page 1.65 f l = −6.6 f a = −99 cm Nature of the lens: Diverging/ behaves like a concave lens. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 27 ¥ 55/2, Set 1 Case Based Question [1 mark each] When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, www.cbse.page www.cbse.page the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the two surfaces. This angle of incidence is called the critical angle for the pair of media www.cbse.page www.cbse.page involved. (i) For a ray incident at the critical angle, the angle of reflection is : ◦ ◦ ◦ ◦ (A) 0 (B) < 90 (C) > 90 (D) 90 (ii) A ray of light µ of¶wavelength 600 nm is incident www.cbse.page www.cbse.page 4 in water n = on the water-air interface at 3 an angle less than the critical angle. The wavelength associated with the refracted ray is (A) 400 nm (B) 450 nm (C) 600 nm www.cbse.page (D) 800 nm www.cbse.page  www.cbse.page www.cbse.page (iii) The interface AB between the two media A and B is shown in the figure. In the denser medium A , the incident ray PQ makes an ◦ angle of 30 with the horizontal. The refracted ray is parallel to the interface. The refractive index of medium B w.r.t. medium A is www.cbse.page www.cbse.page www.cbse.page www.cbse.page p p 3 5 4 2 (A) (B) (C) p (D) p 2 2 3 3 OR www.cbse.page www.cbse.page Two media A and B are separated by a plane boundary. The speed of light in medium A and 8 −1 8 −1 B is 2 × 10 ms and 2.5 × 10 ms respectively. The critical angle for a ray of light going from medium A to medium B is : www.cbse.page www.cbse.page  −1 1 −1 4 www.cbse.page www.cbse.page (A) sin (B) sin 2 5 −1 3 −1 2 (C) sin (D) sin 5 5 (iv) The figure shows the path of a light ray through a triangular prism. In this www.cbse.page www.cbse.page phenomenon, the angle θ is given by : −1 p (A) sin 2 n −1 −1 ¡ 2 ¢ (B) sin n − 1 " # −1 1 (C) sin p www.cbse.page www.cbse.page 2 n −1 " # −1 1 (D) sin ¡ 2 ¢ n −1 Answer A 4 Marks www.cbse.page www.cbse.page (i) Since no option is correct, award 1 mark was awarded to all students. (ii) (D) 800 p nm 3 −1 4 (iii) (A) OR section (B) (B) sin 2 p 5 −1 2 (iv) (A) sin n −1 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 28 ¥ 55/2, Set 1 (i) Draw a labelled ray diagram of a compound microscope showing image formation at least distance of distinct vision. Derive an expression for its magnifying power. www.cbse.page www.cbse.page (ii) A telescope consists of two lenses of focal length 100 cm and 5 cm. Find the magnifying power when the final image is formed at infinity. www.cbse.page www.cbse.page Answer A 5 Marks www.cbse.page www.cbse.page www.cbse.page www.cbse.page (i) www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page The magnification obtained by eye-piece lens à ! D me = 1 + fe The magnification obtained by objective lens v0 m0 = www.cbse.page −u 0 www.cbse.page Hence the total magnifying power is à ! v0 D m = m0 × me = 1+ −u 0 fe www.cbse.page www.cbse.page  ¯ ¯ ¯f ¯ www.cbse.page www.cbse.page ¯ 0¯ (ii) m = ¯ ¯ ¯ fe ¯ Identification of focal length of objective and eyepiece f 0 = 100cm f e = 5cm www.cbse.page www.cbse.page ¯ ¯ ¯100¯ m = ¯¯ ¯ = 20 ¯ 5 www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2024 March ¥ 55/1 All Sets www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 29 ¥ 55/1, Set 1 Assertion (A) : Plane and convex mirrors cannot produce real images under any circumstance. Reason (R) : A virtual image cannot serve as an object to produce a real image. www.cbse.page www.cbse.page (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both Assertion (A) and Reason (R) are true, www.cbse.page www.cbse.page but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false and Reason (R) is also false. www.cbse.page www.cbse.page Answer A 1 Marks (d) Assertion (A) is false and Reason (R) is also false. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 30 ¥ 55/1, Set 1 14 Monochromatic light of frequency 5.0 × 10 Hz passes from air into a medium of refractive index 1.5. Find the wavelength of the light (i) reflected, and www.cbse.page www.cbse.page (ii) refracted at the interface of the two media. OR A plano−convex lens of focal length 16 cm is made of a material of refractive index 1.4. Calculate the radius of the curved surface of the lens. www.cbse.page www.cbse.page Answer A 2 Marks (i) v = vλ 8 14 3 × 10 = 5 × 10 × λ www.cbse.page www.cbse.page −7 λ = 600 nm or 6 × 10 m λair (ii) λmedium = µ 600 nm −7 λmedium = = 400 nm or 4 × 10 m 1.5 www.cbse.page OR www.cbse.page  µ www.cbse.page ¶ www.cbse.page 1 1 1 = (µ − 1) − f R1 R2 µ ¶ 1 1 1 = (1.4 − 1) − 16 R ∞ 1 1 = 0.4 × 16 R www.cbse.page www.cbse.page R = 16 × 0.4 = 6.4 cm š 2024 PYQ 31 ¥ 55/1, Set 1 An object is placed 30 cm in front of a concave mirror of radius of curvature 40 cm. Find the (i) position of the image formed and www.cbse.page www.cbse.page (ii) magnification of the image. Answer A 2 Marks 1 1 1 (i) + = v u fwww.cbse.page www.cbse.page 1 1 1 + = v −30 −20 On solving v = −60 cm µ ¶ v −60 (ii) m = − = − = −2 u −30 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 32 ¥ 55/1, Set 1 Case Based question (each Qn. 1 mark) A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined www.cbse.page www.cbse.page by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination www.cbse.page www.cbse.page is the algebraic sum of the powers of the individual lenses. (i) A double−convex lens, with each face having same radius of curvature R, is made of glass of www.cbse.page www.cbse.page refractive index n. Its power is : 2(n − 1) (2n − 1) (a) (b) R R (n − 1) (2n − 1) (c) (d) 2R 2R www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (ii) A double−convex lens of power P , with each face having same radius of curvature, is cut into two equal parts perpendicular to its principal axis. The power of one part of the lens will be : www.cbse.page P www.cbse.page (a) 2 P (b) P (c) 4 P (d) 2 (iii) The above two parts are kept in contact with each other as shown in the figure. The power of the combination will be : www.cbse.page www.cbse.page www.cbse.page www.cbse.page P P (a) (b) P (c) 2 P (d) 2 4 (iv) A double−convex lens of power P , with each face having same radius of curvature, is cut along its principal axis. The two parts are www.cbse.page www.cbse.page  www.cbse.page www.cbse.page arranged as shown in the figure. The power of the combination will be : www.cbse.page www.cbse.page P (a) Zero (b) P (c) 2 P (d) 2 OR (iv) Two convex lenses of focal lengths 60 cm and 20 cm are held coaxially in contact with each www.cbse.page www.cbse.page other. The power of the combination is : 1 1 (a) 6.6D (b) 15 D (c) D (d) D 15 80 Answer A 4 Marks 2(n − 1) www.cbse.page www.cbse.page (i) (a) R P (ii) (d) 2 (iii) (b) P (iv) (c) 2 P OR (a) 6.6D www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 33 ¥ 55/1, Set 1 (i) A ray of light passes through a triangular prism. Show graphically, how the angle of deviation varies with the angle of incidence ? Hence define the angle of minimum deviation. www.cbse.page www.cbse.page (ii) A ray of light is incident normally on a refracting face of a prism of prism angle A and suffers a deviation of angle δ. Prove that the refractive index n of the material of the prism is given by www.cbse.page www.cbse.page sin(A + δ) n= sin A (iii) The refractive index of the material of a prism p is 2. If the refracting angle of the prism is 60°, find the www.cbse.page www.cbse.page (1) Angle of minimum deviation, and (2) Angle of incidence. Answer A 5 Marks www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page (i) www.cbse.page www.cbse.page Minimum deviation angle is defined as the angle at which angle of incidence is equal to the angle of emergence. Alternatively : At minimum deviation refracted ray inside the prism becomes parallel to the base of the prism. www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page (ii) At the face XZ :- www.cbse.page www.cbse.page µ sin i = 1 × sin r......(1) r = i + δ [ from diagram ]......(2) In △X M N ; A + (90 − i ) + 90 = 180 ⇒A=i......(3) Putting eq. (3) & (2) in eq. (1) www.cbse.page www.cbse.page µ sin A = sin(A + δ) sin(A + δ) µ= sin A www.cbse.page www.cbse.page (iii) (1) www.cbse.page www.cbse.page µ ¶ A + δm sin 2 µ= A sin µ 2 ¶ 60 + δm p sin 2 2= www.cbse.page www.cbse.page sin 30 ◦ µ ¶ 60 + δm 1 ◦ ⇒ sin = p = sin 45 2 2 60 + δm ◦ ◦ ⇒ = 45 ⇒ δm = 30 2 www.cbse.page www.cbse.page A + δm 60 + 30 ◦ (2) i= = = 45 2 2 www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2024 March ¥ 55 B www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 34 ¥ 55 B, Set 1 Assertion (A) : Signals through an optical fibre can be transmitted without any appreciable loss of energy. Reason (R) : An optical fibre works on the www.cbse.page www.cbse.page principle of total internal reflection. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). www.cbse.page www.cbse.page (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, Reason (R) is also false. www.cbse.page www.cbse.page Answer A 1 Marks (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 35 ¥ 55 B, Set 1 Name the factors on which focal length of a lens depends. How will a thin biconvex glass lens submerged in water behave ? Give reason for your answer. www.cbse.page www.cbse.page Answer A 2 Marks Two factors : ¥ Radius of curvature ¥ Refractive index of the material of the lens www.cbse.page www.cbse.page w.r.t. the surroundings Nature of the lens will not change but the focal length will increase Reason : www.cbse.page www.cbse.page Focal length of a lens is inversely proportional to the refractive index of the material of lens w.r.t. the surroundings. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 36 ¥ 55 B, Set 1 The power of the combination of two thin convex lenses L1 and L2, kept coaxially in contact, is +10 D. If the focal length of L1 is four times that of L2, find their focal lengths. www.cbse.page www.cbse.page Answer A 2 Marks 1 1 1 = + f f1 f2 f1 = 4f2 (given) 1 1 1 www.cbse.page www.cbse.page P= = + f 4f2 f2 5 10 = 4f2 50 f2 = cm 4 ∴ f1 = 50 cm www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 37 ¥ 55 B, Set 1 Case Based Question In a homogeneous medium, light travels along a straight line path. But when a ray of light travels from one medium to another, it deviates from its www.cbse.page www.cbse.page initial path. This bending of light is called refraction of light. The extent to which a ray deviates in medium 2 from its initial path in medium 1, is determined by the refractive index of medium 2 with respect to medium 1. The www.cbse.page www.cbse.page refractive index is also related to the ratio of speeds of light in the two media. The phenomenon of total internal reflection occurs when light passes from a denser medium into a rarer medium and the angle of incidence www.cbse.page www.cbse.page exceeds the critical angle for the given pair of media. (i) A ray of monochromatic light of wavelength λ and speed v travels from air into a glass slab. Inside the glass slab, www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (a) both λ and v decrease (b) both λ and v increase (c) λ decreases and v increases (d) λ increases and v decreases (ii) A ray of light travelling from air into a medium, www.cbse.page www.cbse.page ◦ is incident on the interface at an angle of 45. ◦ If the ray deviates by 15 from its initial path, the refractive index of the medium is : p p p (a) 2 (b) 2 (c) 2 2 (d) 3 OR www.cbse.page www.cbse.page (ii) A point source of light is kept at the bottom of a tank filled with a transparent liquid up to a height H. If the radius of the circular patch on the surface from which light can come out is H www.cbse.page www.cbse.page p , the refractive index of the liquid is close to 3 (a) 1.3 (b) 1.5 (c) 1 · 7 (d) 2 · 0 (iii) In an optical fiber, the refractive indices of the core and cladding are µ1 and µ2 respectively. Then : www.cbse.page www.cbse.page  (a) µ1 = µ2 www.cbse.page www.cbse.page (b) µ1 < µ2 (c) µ1 is slightly greater than µ2 (d) µ1 is large compared to µ2 (iv) Light of wavelength λ travelling with speed c www.cbse.page www.cbse.page in air, enters a medium of refractive index µ. The frequency of light in the medium is : c µc µλ c (a) (b) (c) (d) µλ λ c λ Answer www.cbse.page A 4 Marks www.cbse.page (i) (a) both λ and v decrease p (ii) (b) 2 OR (ii) (d) 2 · 0 www.cbse.page www.cbse.page (iii) (c) µ1 is slightly greater than µ2 c (iv) (d) λ www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š 2024 PYQ 38 ¥ 55 B, Set 1 (i) What are coherent sources of light ? Briefly explain how a pair of coherent sources are obtained in a Young’s double-slit experiment. Mention the conditions for constructive and www.cbse.page www.cbse.page destructive interferences in this experiment. This question is of Chapter 10. Beaware of change in question pattern. It happens in every set of question paper where 2 or 3 chapters are mixed in one question www.cbse.page www.cbse.page (ii) An object is kept 20 cm from a convex mirror of radius of curvature 60 cm. Find the position of the image formed. Will the image be real or virtual ? www.cbse.page OR www.cbse.page (i) Answer the following giving reasons : (1) In modern microscopes, multicomponent lenses are used for both the objective and the eyepiece. (2) In a compound microscope, both the www.cbse.page www.cbse.page  www.cbse.page www.cbse.page objective and the eyepiece have small focal lengths. (3) When viewing through a compound microscope, our eyes should be positioned not on the eyepiece, but a short distance away www.cbse.page www.cbse.page from it for best viewing. (ii) Two students are separated by a 6 m partition wall in a room 9 m high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each www.cbse.page www.cbse.page other, though they can talk easily ? Answer A 5 Marks (i) Coherent light sources are those sources which emit light waves with the same www.cbse.page www.cbse.page frequency/wavelength and have a constant phase difference. A pair of coherent sources is obtained in Young’s Double Slit Experiment by illuminating two identical narrow slits by a www.cbse.page www.cbse.page  www.cbse.page www.cbse.page monochromatic source of light equidistant from the slits. For Constructive Interference: Phase difference = 2nπ www.cbse.page n = 0, 1, 2,.......... www.cbse.page Path difference = nλ n = 0, 1, 2,.......... For Destructive Interference: Phase difference = (2n + 1)π www.cbse.page www.cbse.page n = 0, 1, 2.......... µ ¶ 1 Path difference = n + λ 2 n = 0, 1, 2,.......... (ii) u = −20 cm R www.cbse.page www.cbse.page f = = 30 cm 2 1 1 1 + = v u f µ ¶ 1 1 1 + − = v 20 30 www.cbse.page www.cbse.page  1 1 1 3+2 5 www.cbse.page www.cbse.page = + = = v 30 20 6 60 v = 12 cm Virtual Image. OR (1) To improve image quality by minimizing www.cbse.page www.cbse.page various optical aberrations in lenses. (2) To achieve large magnification Magnifying Power à !à ! L D m= www.cbse.page f0 fe www.cbse.page (3) Because of this position our eye will collect all the light refracted by the objective which results in relaxation of the eye. OR www.cbse.page www.cbse.page To increase the field of view & for relaxation of eye. (ii) For diffraction or bending of a wave, size of the aperture should be comparable to the wavelength. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page The wavelength of sound is comparable to the size of the aperture whereas wavelength of light is much smaller than size of the aperture so bending of sound will take place but bending of light will not occur. Therefore students are unable to see each other though www.cbse.page www.cbse.page they can talk easily. www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ¢ 2023 to 2019 PYQs www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ CBSE SQP 2024 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š Question 1 Assertion (A) : Propagation of light through an optical fibre is due to total internal reflection taking place at the core-cladding interface. Reason (R) : Refractive index of the material of the www.cbse.page www.cbse.page cladding of the optical fibre is greater than that of the core. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but www.cbse.page www.cbse.page Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false and Reason (R) is also false. A Answerwww.cbse.page ¥ Set 1, 1 Marks www.cbse.page Assertion (A) is true, but Reason (R) is false. The refractive index of the material of the core is higher than that of the cladding. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page Theory Recap Optical fibres are fabricated with high quality composite glass/quartz fibres. Each fibre consists of a core and cladding. The refractive index of the material of the core is higher than that of the cladding. www.cbse.page www.cbse.page š Question 2 A ray of monochromatic light passes through an equilateral glass prism in such a way that the angle of incidence is equal to the angle of emergence and each of these angles is 3/4 times the angle of www.cbse.page www.cbse.page the prism. Determine the angle of deviation and the refractive index of the glass prism. A Answer ¥ Set 1, 2 Marks ◦ Here angle of prism A = 60 , Angle of incidence i = Angle of emergence e www.cbse.page www.cbse.page and under this condition angle of deviation is minimum 3 3 ∴ i = e = A = × 60 = 45 and i + e = A + D, ◦ ◦ 4 4 ◦ ◦ ◦ hence Dm = 2i − A = 2 × 45 − 60 = 30 ∴ Refractive index of glass prism www.cbse.page www.cbse.page  µ ¶ www.cbse.page µ ◦ ◦ ¶ www.cbse.page A + Dm 60 + 30 sin sin 2 2 n= µ ¶ = µ ◦¶ A 60 sin sin 2 2 ◦ p sin 45 1/ 2 p = = = 2 sin 30◦ 1/2 www.cbse.page www.cbse.page š Question 3 Show that the least possible distance between an object and its real image in a convex lens is 4 f , where f is the focal length of the lens. A Answerwww.cbse.page ¥ Set 1, 2 Marks www.cbse.page www.cbse.page www.cbse.page Let d be the least distance between object and image for a real image formation. www.cbse.page www.cbse.page 1 1 1 www.cbse.page www.cbse.page = − f v u 1 1 1 d = + = f x d − x x(d − x) 2 f d = xd − x 2 x −dx + f d = 0 www.cbse.page www.cbse.page p 2 d ± d −4f d x= 2 For real roots of x, ¯ 2 ¯ d −4f d ≥ 0 ¯ d ≥ 4f š OR www.cbse.page www.cbse.page In an astronomical telescope in normal adjustment a straight black line of length L is drawn on the objective lens. The eyepiece forms a real image of this line whose length is l. What is the angular magnification of the telescope? www.cbse.page www.cbse.page A Answer ¥ Set 1, 2 Marks Let f 0 and f e be the focal length of the objective and eyepiece respectively. For normal adjustment the distance from objective to eyepiece is f 0 + f e. Taking the line on the objective as object and eyepiece as lens www.cbse.page www.cbse.page  ¡ ¢ www.cbse.page www.cbse.page u = − f0 + fe and f = fe ¯ à ! 1 1 1 ¯ f o + f e − = ¯ v= fe v [−( f 0 + f e )] f e ¯ f o Linear magnification (eyepiece) v Image size f e l = = = = u object size f o L www.cbse.page www.cbse.page ∴ Angular magnification of telescope f0 L M= = fe l š Question 4 Case Based Question www.cbse.page www.cbse.page Types of Lenses and their combination A convex or converging lens is thicker at the centre than at the edges. It converges a beam of light on refraction through it. It has a real focus. Convex lens is of three types: Double convex lens, Plano www.cbse.page www.cbse.page convex lens and Concavo-convex lens. Concave lens is thinner at the centre than at the edges. It diverges a beam of light on refraction through it. It has a virtual focus. Concave lenses are of three types: Double concave lens, Plano concave lens and Convexo-concave lens. When two thin lenses www.cbse.page www.cbse.page  www.cbse.page www.cbse.page of focal lengths f 1 and f 2 are placed in contact with each other along their common principal axis, then the two lens system is regarded as a single lens of focal length f and 1 1 1 = + f f1 f2 If several thin lenses of focal length f 1, f 2,.... f n are www.cbse.page www.cbse.page placed in contact, then the effective focal length of the combination is given by 1 1 1 1 = + +..... + f f1 f2 fn and in terms of power, we can write www.cbse.page www.cbse.page P = P1 + P2 +.... + Pn The value of focal length and power of a lens must be used with proper sign consideration. (i) Two thin lenses are kept coaxially in contact with each other and the focal length of the combination is 80 cm. If the focal length of one www.cbse.page www.cbse.page lens is 20 cm, the focal length of the other would be (a) −26.7cm (b) 60cm (c) 80cm (d) 30cm A Answer ¥ Set 1, 1 Marks Given, f = 80 cm, f 1 = 20 cm www.cbse.page www.cbse.page  1 1 1 www.cbse.page www.cbse.page = + f f1 f2 1 1 1 = + 80 20 f 2 1 1 1 1 − 4 −3 = − = = f 2 80 20 80 www.cbse.page 80 www.cbse.page −80 f2 = = −26.7 cm 3 (ii) A spherical air bubble is embedded in a piece of glass. For a ray of light passing through the bubble, it behaves like a (a) converging lens www.cbse.page www.cbse.page (b) diverging lens (c) mirror (d) thin plane sheet of glass A Answer ¥ Set 1, 1 Marks it behave like a diverging lines due to refraction in www.cbse.page www.cbse.page the glass. (iii) Lens generally used in magnifying glass is (a) single concave lens (b) single convex lens (c) combination of convex lens of lower power and concave lens of lower focal length www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (d) Planoconcave lens A Answer ¥ Set 1, 1 Marks single convex lens (iv) The magnification of an image by a convex lens is positive only when the object is placed www.cbse.page www.cbse.page (a) at its focus F (b) between F and 2F (c) at 2F (d) between F and optical centre A Answer ¥ Set 1, 1 Marks www.cbse.page www.cbse.page between F and optical centre OR A convex lens of 20 cm focal length forms a real image which is three times magnified. The distance of the object from the lens is (a) 13.33 cm www.cbse.page (b) 14 cmwww.cbse.page (c) 26.66 cm (d) 25 cm A Answer ¥ Set 1, 1 Marks Given, f = 20 cm v ¯ v ¯ ¯ ¯ m= ¯ 3= ¯ v = 3u u u www.cbse.page www.cbse.page  1 1 1 www.cbse.page www.cbse.page − = v u f 1 1 1 − = 3u −u 20 1+3 1 = 3u 20 80 www.cbse.page www.cbse.page u = = 26.6 cm 3 š Question 5 (i) Draw a ray diagram for the formation of image of a point object by a thin double convex lens having radii of curvature R1 and R2. Hence www.cbse.page www.cbse.page derive lens maker’s formula. (ii) A converging lens has a focal length of 10 cm in air. It is made of a material of refractive index 1.6. If it is immersed in a liquid of refractive index 1.3, find its new focal length. www.cbse.page www.cbse.page A Answer ¥ Set 1, 5 Marks www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page (i) When a ray refracts from a lens (double convex), in above figure, then its image formation can be seen in term of two steps : www.cbse.page www.cbse.page Step 1: The first refracting surface forms the image I 1 of the object O www.cbse.page www.cbse.page Step 2: The image of object O for first surface acts like a virtual object for the second surface. Now for the first surface ABC, ray will move from rarer to denser medium, then www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page n2 n1 n2 − n1 + = B I 1 OB BC 1 Similarly for the second interface, ADC we can www.cbse.page www.cbse.page write. n1 n2 n2 − n1 − = D I D I1 DC 2 DI 1 is negative as distance is measured against the direction of incident light. Adding both the equation, we get n2 n1 n1 n2 n2 − n1 n2 − n1 www.cbse.page www.cbse.page + + − = + B I 1 OB D I D I 1 BC 1 DC 2 µ ¶ n1 n1 1 1 + = (n 2 − n 1) + D I OB BC 1 DC 2 ¡ ∵ for thin lens B I 1 = D I 1) Now, if we assume the object to be at infinity i.e. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page OB → ∞, then its image will form at focus F (with focal length f ), i.e. DI = f Thus equation can be rewritten as µ ¶ n1 n1 1 1 + = (n 2 − n 1) + f ∞ BC 1 DC 2 µ ¶ n1 1 1 = (n 2 − n 1) www.cbse.page + www.cbse.page f BC 1 DC 2 Now according to the sign conventions BC 1 = +R 1 and DC 2 = −R 2 Substituting the equation , we get µ ¶ n1 1 1 = (n 2 − n 1) − f www.cbse.page R1 R2 www.cbse.page µ ¶µ ¶ 1 n2 1 1 = −1 − f n1 R1 R2 µ ¶ 1 1 1 = (n 21 − 1) − f R1 R2 µ ¶ 1 1 1 (ii) = (1.6 − 1) www.cbse.page − www.cbse.page fa R1 R2 · ¸µ ¶ 1 1.6 1 1 = −1 − fℓ 1.3 R1 R2 · ¸ fℓ 0.6 = × 1.3 fa 0.3 f ℓ = 2.6 × 10 cm = f ℓ = 26 cm www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page www.cbse.page ◎ 2023 July ¥ 55/C All Sets www.cbse.page www.cbse.page  www.cbse.page www.cbse.page § 2023 55/C Compart š Question 6 A small object lies at the bottom of a vessel filled with water (refractive index 4/3) up to a height H. When viewed from a point above the surface of www.cbse.page www.cbse.page water, the object appears raised by n percent of H. The value of n is (a) 15 (b) 20 (c) 25 (d) 33 A Answer ¥ Set 1, 1 Marks 1 1 n air = = www.cbse.page www.cbse.page n water 4/3 Object appears to be raised by 25% of H š Question 7 (i) Draw a labelled ray diagram of an astronomical telescope to show the image formation of a www.cbse.page www.cbse.page distant object by it in normal adjustment. What are the main considerations required in selecting the objective and eyepiece lenses so that the telescope has large magnifying power and high resolution? www.cbse.page www.cbse.page  www.cbse.page www.cbse.page (ii) A biconvex lens of focal length 20 cm is immersed in water, whose refractive index is 4/3. Find the change, if any, in the nature and the focal length of the lens. Refractive index of the material of convex lens is 3/2. A Answerwww.cbse.page ¥ Set 1, 5 Marks www.cbse.page www.cbse.page www.cbse.page (i) For large magnifying power fo > fe www.cbse.page www.cbse.page For high resolution aperture of objective should be large · ¸ 1 ¡ ¢ 1 1 (ii) = n g − 1 − fa R1 R2 µ ¶· ¸ 1 ng 1 1 = −1 − fa nw R1 R2 www.cbse.page www.cbse.page  ¡ ¢ www.cbse.page www.cbse.page fw ng − 1 =µ ¶ fa ng −1 nw µ ¶ 3 −1 fw 2 1/2 =µ ¶= =4 20 3 3 1/8 × −1 www.cbse.page www.cbse.page 2 4 fw = 80 cm Changes in focal length ∆ f = 80 − 60 = 20 cm www.cbse.page www.cbse.page Nature of the lense is converging because f w is positive š OR (i) Draw a ray diagram showing refraction of light through a prism of angle A and obtain the www.cbse.page www.cbse.page relation between µ, A and the angle of minimum deviation δm. (ii) An equiconvex lens of radius of curvature R and made of glass of refractive index µ is cut into two identical plano-convex lenses. Find the focal length of the plano-convex lenses. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page A Answer ¥ Set 1, 5 Marks www.cbse.page www.cbse.page (i) From the figure ∠A + ∠QNR = 180 www.cbse.page ◦www.cbse.page From △QNR r1 + r2 + ∠QNR = 180 ◦ comparing the above equations r1 + r2 = A...(1) www.cbse.page www.cbse.page δ = (i − r1) + (e − r2) δ = i + e − A...(2) At the minimum derivation Dm δ = Dm, i = e and r1 = r2 www.cbse.page www.cbse.page  From equation (1) www.cbse.page www.cbse.page 2r = A A r= 2 From equation (2) www.cbse.page Dm = 2i − A www.cbse.page A + Dm i= 2 The refractive index of the prism is · ¸ (A + Dm ) sin sin i 2 n21 = = · ¸ sin r A www.cbse.page sin www.cbse.page 2 · ¸ 1 1 1 (ii) = (n − 1) − f R1 R2 · ¸ 1 2 = (n − 1) f1 R · ¸ 1 1 www.cbse.page www.cbse.page = (n − 1) f2 R f2 = 2 f1 www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š Question 8 A bright point source is placed at the bottom of a tank containing a transparent liquid (refractive index µ ) to a height H. Let r be the radius of the circular area of the liquid surface through which light can emerge out. Find the ratio (r/H). www.cbse.page www.cbse.page A Answer ¥ Set 2, 2 Marks 1 sin i c = µ p p µ2 − 1 2 cos i c = 1 − sin i = www.cbse.page µ www.cbse.page 1 tan i c = p 2 µ −1 r 1 =p H 2 µ −1 š Question 9 www.cbse.page www.cbse.page (a) Draw a ray diagram for formation of a real and diminished image of an object kept in front of a concave mirror. Hence derive the mirror equation. (b) A concave mirror of focal length 10 cm produces a real image which is 3 times the size www.cbse.page www.cbse.page  www.cbse.page www.cbse.page of the object. Find the distance of the object from the mirror. A Answer ¥ Set 2, 5 Marks www.cbse.page www.cbse.page www.cbse.page www.cbse.page ′ ′ (a) ∆A B F ∼ ∆M P F ′ ′ ′ BA BF = (∵ P M = AB )...(1) BA FP ′ ′ Also ∆A B P ∼ ∆AB P www.cbse.page www.cbse.page ′ ′ ′ BA BP =...(2) BA BP Comparing eq. (1) and (2) ′ ′ ′ B F B P −FP B P = = FP FP FP ′ B P = −v www.cbse.page www.cbse.page  www.cbse.page www.cbse.page FP = −f B P = −u 1 1 1 On solving we get, = + f v u 1 1 1 (b) = + f v u 1 1 1 www.cbse.page www.cbse.page = − u f v v − = −3 u v = 3u 1 1 1 = − u f 3uwww.cbse.page www.cbse.page 1 1 1 + = u 3u f 4 1 = 3u f 4f 40 u= = − cm www.cbse.page www.cbse.page 3 3 š OR (a) Two converging lenses of focal lengths f 1 and f 2 are placed coaxially in contact. Derive the expression for the focal length of the www.cbse.page www.cbse.page  www.cbse.page www.cbse.page combination using the ray diagram for the formation of the image of an object by the combination. (b) The figure shows the variation of image distance v with object distance u for a lens. (i) What is the nature of the lens ? www.cbse.page www.cbse.page (ii) Using the graph, find the focal length of the lens. www.cbse.page www.cbse.page www.cbse.page www.cbse.page A Answer ¥ Set 2, 5 Marks (a) Image formed by the first lens A, 1 1 1 − =..........(1) v u f1 Image formed by second lens B, www.cbse.page www.cbse.page  1 1 1 www.cbse.page www.cbse.page − =..........(2) v v1 f2 Adding eq (1) and (2), 1 1 1 1 we get, − = +..........(3) v u f1 f2 If the two lens system is regarded as equivalent www.cbse.page www.cbse.page to a single lens of focal length f , we have 1 1 1 − =..........(4) v u f From equation (3) and (4), we get 1 1 1 = + www.cbse.page www.cbse.page f f1 f2 (b.i) From graph we see that as the object moves away from the lens the image comes nearer. Therefore it is a convex lens (b.ii) u = −20 cm 40 www.cbse.page www.cbse.page v= cm 3 1 1 1 3 1 = − = + f v u 40 20 f = 8 cm www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š Question 10 (i) Draw a ray diagram to show the formation of image by a concave mirror when the object is placed between f and 2 f. Using this diagram, derive the mirror equation. (ii) An object is kept 30 cm in front of a convex www.cbse.page www.cbse.page mirror of focal length 12 cm. Find the nature and position of the image formed. A Answer ¥ Set 3, 5 Marks www.cbse.page www.cbse.page www.cbse.page www.cbse.page ′ ′ ′ (i) From ∆A B C ∼ ∆DP F ′ ′ ′ BA BF = (∵ P D = AB )....(1) BA FP ′ ′ Form △A B P ∼ △AB P ′ ′ ′ BA BP =....(2) BA www.cbse.page BP www.cbse.page  www.cbse.page www.cbse.page Comparing equation (1) and (2) ′ ′ ′ B F B P −FP B P = = FP FP BP ¯ ¯ ′ Here B P = −v ¯ FP = −f ¯ B P = −u −v + f −v = −f −u www.cbse.page www.cbse.page v−f v = f u v v = 1+ f u 1 1 1 On solving we get = + ¯ www.cbse.page f v u www.cbse.page (ii) u = −30 cm ¯ f = +12 cm 1 1 1 = + f v u 1 1 1 = − v f u 1 1 1 7 = + = www.cbse.page www.cbse.page v 12 30 60 60 v= cm 7 Since v is positive image is virtual and erect. www.cbse.page www.cbse.page  www.cbse.page www.cbse.page š OR (i) Draw a ray diagram showing the image formation by a compound microscope. Hence obtain the expression for total magnification when the image is formed at least distance of distinct vision. www.cbse.page www.cbse.page (ii) A compound microscope consists of an objective lens of focal length 2 cm and an eyepiece of focal length 6 cm. If they are separated by a distance of 24 cm, find the total magnification when the image is formed at infinity. www.cbse.page www.cbse.page A Answer ¥ Set 3, 5 Marks www.cbse.page www.cbse.page www.cbse.page www.cbse.page  www.cbse.page www.cbse.page www.cbse.page www.cbse.page (i) Magnification due to objective www.cbse.page www.cbse.page à ! ′ ?