NEET Physics Notes - Chapter 29 Ray Optics PDF
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These notes provide an overview of Ray Optics, focusing on concepts and formulas. The material covers various topics, including reflection and refraction principles.
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60 1636 Ray Optics Chapter E3 29 Ray Optics O (Virtual object) (Real object) Real image The image formed by a plane mirror is virtual, erect, laterally inverted, equal in size that of the object and at a distance equal to the distance of the object in front of the mirror. I (Virtual image) D YG (Rea...
60 1636 Ray Optics Chapter E3 29 Ray Optics O (Virtual object) (Real object) Real image The image formed by a plane mirror is virtual, erect, laterally inverted, equal in size that of the object and at a distance equal to the distance of the object in front of the mirror. I (Virtual image) D YG (Real image) O Reflection From a Plane Surface (Plane Mirror) U If light rays, after reflection or refraction, actually meets at a point then real image is formed and if they appears to meet virtual image is formed. I (3) There is a phase change of if reflection takes place from denser medium. ID Real and Virtual Images x x Fig. 29.2 (1) Deviation () : Deviation produced by a plane mirror and by two inclined plane mirrors. (Virtual image) i (Real image) U (Virtual object) (Virtual image) ST I Reflection of Light When a ray of light after incidenting on a boundary separating two media comes back into the same media, then this phenomenon, is called reflection of light. = (180 – 2i) Incident ray i = (360 – 2) (B) Double Reflection (A) Single Reflection Fig. 29.3 (2) Images by two inclined plane mirrors : When two plane mirrors are inclined to each other at an angle , then number of images (n) formed of an object which is kept between them. 360 o 360 o n 1 ; If even integer (i) Normal Reflected ray (Real object) O r (ii) If 360 o odd integer then there are two possibilities r Boundary Object Fig. 29.1 (1) i = r (2) After reflection, velocity, wave length and frequency of light remains same but intensity decreases. Object /2 /2 (A) Object is placed symmetrically (B) Object is placed asymmetrically Fig. 29.4 Ray Optics 1637 360 n 1 (v) Focus (F) : An image point on principle axis for an object at . (vi) Focal length (f) : Distance between P and F. 360 n : f (vii) Relation between f and R (3) Other important informations (f = –ve , f = + ve , f = ) (viii) Power : The converging or diverging ability of mirror (ix) Aperture : Effective diameter of light reflecting area. Intensity of image Area (Aperture) (x) Focal plane : A plane passing from focus and perpendicular to principle axis. (2) Sign conventions : concave (ii) When mirror moves towards the stationary object with speed u, the image will move with speed 2u in same direction as that of mirror. convex plane 2 60 (i) When the object moves with speed u towards (or away) from the plane mirror then image also moves towards (or away) with speed u. But relative speed of image w.r.t. object is 2u. Incident ray u I O 2u Rest u Mirror is moving (A) (B) Mirror or Lens Fig. 29.5 (iv) To see complete wall behind himself a person requires a plane mirror of at least one third the height of wall. It should be noted that person is standing in the middle of the room. h h 3 M' D YG M' B L d (A) Curved Mirror d (B) Fig. 29.6 It is a part of a transparent hollow sphere whose one surface is polished. C C P U P F Fig. 29.8 (ii) Distances measured in the direction of incident rays are taken as positive while in the direction opposite of incident rays are taken negative. (iii) Distances above the principle axis are taken positive and below the principle axis are taken negative. Table 29.1 : Useful sign Concave mirror M' h E h 2 – (i) All distances are measured from the pole. U H E M' Principle axis ID (iii) A man of height h requires a mirror of length at least equal to h/2, to see his own complete image. H E + – u Mirror at rest + E3 I O R 2 Real image (u ≥ f) Convex mirror Virtual image (u< f) Distance of object u – u – u – Distance of image v – v + v + f – f O+ O + Focal length f – Height of object O + I + I Radius of curvature R – R – R + Magnification m – m+ m + Height of image I – + + Image Formation by Curved Mirrors F Principal axis ST Concave mirror Convex mirror Fig. 29.7 Concave mirror converges the light rays and used as a shaving mirror, In search light, in cinema projector, in telescope, by E.N.T. specialists etc. Convex mirror diverges the light rays and used in road lamps, side mirror in vehicles etc. (1) Terminology (i) Pole (P) : Mid point of the mirror (ii) Centre of curvature (C) : Centre of the sphere of which the mirror is a part. (iii) Radius of curvature (R): Distance between pole and centre of curvature. (R = –ve , R = +ve , R = ) (iv) Principle axis : A line passing through P and C. concave convex plane Concave mirror : Image formed by concave mirror may be real or virtual, may be inverted or erect, may be smaller, larger or equal in size of object. (1) When object is placed at infinite (i.e. u = ) Image At F Real Inverted Very small in size F Fig. 29.9 P 1638 Ray Optics Magnification m 2f) Small in size Magnification m < + 1 Mirror Formula and Magnification Image Between F and C Real Inverted Small in size m–1 F P (* Always use sign convention while solving the problems) Axial magnification : When object lies along the principle axis then its I (v 2 v 1 ) axial magnification m O (u 2 u 1 ) ID U ms D YG Image At P Real C F Inverted Very large in size m >> – 1 (6) When object is placed between focus Fig. and29.13 pole (i.e. u < f) P U F ST Fig. 29.14 Convex mirror : Image formed by convex mirror is always virtual, erect and smaller in size. (1) When object is placed at infinite (i.e. u = ) Image At F Virtual Erect Very small in size Magnification m +1 60 (2) Lateral magnification : When an object is placed perpendicular to the principle axis, then linear magnification is called lateral or transverse magnification. E3 Image At C Real Inverted Equal in size m=–1 1 1 1 f v u P Fig. 29.16 F C A Area of image ( Ai ) ms m 2 i Ao Area of object ( Ao ) Ray Optics 1639 Refraction of Light The bending of the ray of light passing from one medium to the other medium is called refraction. (3) Absolute refractive index : When light travels from vacuum to any transparent medium then refractive index of medium w.r.t. vacuum is called c it’s absolute refractive index i.e. vacuum medium v Absolute refractive indices for glass, water and diamond are 3 4 12 respectively g 1.5, w 1.33 and D 2.4 2 3 5 (4) Relative refractive index : When light travels from medium (1) to medium (2) then refractive index of medium (2) w.r.t. medium (1) is called v it’s relative refractive index i.e. 1 2 2 1 (where v and v are the 1 v 2 speed of light in medium 1 and 2 respectively). (5) When we say refractive index we mean absolute refractive index. (6) The minimum value of absolute refractive index is 1. For air it is very near to 1. ( ~ 1.003 ) (C) Fig. 29.17 2 (1) The refraction of light takes place on going from one medium to (A) another because the speed of light is different in the two media. (2) Greater the difference in the speeds of light in the two media, greater will be the amount of refraction. (3) A medium in which the speed of light is more is known as optically rarer medium and a medium is which the speed of light is less, is known as optically denser medium. (7) Cauchy’s equation : A Deviation = (i – r) Denser medium D YG Refracted ray 29.18a denser medium to a rarer (5) When a ray of light goesFig. from medium, it bends away from the normal. Denser medium Deviation = (r – i ) i r Rarer medium C 4 ...... (8) If a light ray travels from medium (1) to medium (2), then 1 2 2 1 v 1 1 2 v 2 (9) Dependence of Refractive index (i) Nature of the media of incidence and refraction. (ii) Colour of light or wavelength of light. (iii) Temperature of the media : Refractive index decreases with the increase in temperature. U Rarer medium ID i B 2 (Red violet so Red violet ) (4) When a ray of light goes from a rarer medium to a denser medium, it bends towards the normal. Incident ray U Fig. 29.19 (6) Snell’s law : The ratio of sine of the angle of incidence to the angle of refraction (r) is a constant called refractive index ST sin i i.e. (a constant). For two media, Snell's law can be sin r sini written as 1 2 2 1 sinr 1 sini 2 sinr i.e. sin constant Table 29.2 : Indices of refraction for various substances, Measured with light of vacuum wavelength = 589 nm 0 Substance Refractive index Substance Solids at 20°C Refractive index Liquids at 20°C Diamond (C) 2.419 Benzene 1.501 Fluorite (CaF2) 1.434 Carbon disulfide 1.628 Flused quartz (SiO2) 1.458 Carbon tetrachloride 1.461 Glass, crown 1.52 Ethyl alcohol 1.361 Glass, flint 1.66 Glycerine 1.473 Ice (H2O) (at 0 C) 1.309 Water 1.333 Polystyrene 1.49 Sodium chloride 1.544 Gases at 0°C, 1 atm Air 1.000293 Zircon 1.923 Carbon dioxide 1.00045 o (10) Reversibility of light and refraction through several media Incident ray 1 1 i 2 Also in vector form : ˆi nˆ ( rˆ nˆ ) Refractive Index (1) Refractive index of a medium is that characteristic which decides speed of light in it. (2) It is a scalar, unit less and dimensionless quantity. 2 E3 (B) 60 1 Princ ipal Axis r 3 2 (A) 1 2 1 2 1 (B) 2 1 Fig. 29.20 1 2 3 3 1 1 or 2 3 1 3 1 2 1640 Ray Optics Real and Apparent Depth If object and observer are situated in different medium then due to refraction, object appears to be displaced from it’s real position. (1) When object is in denser medium and observer is in rarer medium (i) h' h (ii) Real depth < Apparent depth. (iii) d ( 1)h h O d O Refraction Through a Glass Slab Real depth h Fig. 29.21 Apparent depth h (1) Lateral shift : The refracting surfaces of a glass slab are parallel to each other. When a light ray passes through a glass slab it is refracted twice at the two parallel faces and finally emerges out parallel to it's incident direction i.e. the ray undergoes no deviation = 0. The angle of emergence (e) is equal to the angle of incidence (i) (ii) Real depth > Apparent depth 1 4 h (iii) Shift d h h' 1 h. For water d ; 3 4 3 h d 2 3 i ID For glass (iv) Lateral magnification : consider an object of height x placed vertically in a medium such that the lower end (B) is a distance h from the interface and the upper end (A) at a distance (h – x) from the interface. 2 1 D YG B Distance of image of B (i.e. ) from the interface = Fig.B'29.22 2 h 1 Distance of image of A (i.e. A') from the interface 2 (h x ) 1 U 2 x 1 ST Apparent depth of bottom combination = 1 2 d3 3 O' t Fig. 29.26 d1 2 d2 d3 Fig. 29.23 2 1 2 than ) 1 2 (2) Object is in rarer medium and observer is in denser medium O d O h h O x = geometrical path and x = optical path 1 3 2 (In case of two liquids if d 1 d 2 1 OO' x 1 t .... d AC d d 2 ..... 1 d d d App. 1 2 .... 1 (2) Normal shift : If a glass slab is placed in the path of a converging or diverging beam of light then point of convergence or point of divergence appears to be shifted as shown Normal shift Time taken by light ray to pass through the medium (v) If a beaker contains various immiscible liquids as shown then d2 M (3) Optical path : It is defined as distance travelled by light in vacuum in the same time in which it travels a given path length in a medium. 1 or, the lateral magnification of the object m 2 1 d1 N MN = t sec r sin (i – r) B' A Therefore, length of the image e The Lateral shift of the ray is the perpendicular distance between the incident and the emergent ray, and itFig. is given 29.25 by Opti cal Axis (h – x) A' rr t U 1 h h h ; Shift for glass d g 2 3 (iv) Shift for water dw E3 (i) 60 h Light x Fig. 29.27 Total Internal Reflection (TIR) x c ; where x Ray Optics 1641 (i) The refractive index of the material of the core ( ) is higher than that of the cladding ( ). (ii) When the light is incident on one end of the fibre at a small angle, the light passes inside, undergoes repeated total internal reflections along the fibre and finally comes out. The angle of incidence is always larger than the critical angle of the core material with respect to its cladding. (iii) Even if the fibre is bent, the light can easily travel through along the fibre (iv) A bundle of optical fibres can be used as a 'light pipe' in medical and optical examination. It can also be used for optical signal transmission. Optical fibres have also been used for transmitting and receiving electrical signals which are converted to light by suitable transducers. 1 When a ray of light goes from denser to rarer medium it bends away from the normal and as the angle of incidence in denser medium increases, the angle of refraction in rarer medium also increases and at a certain angle, angle of refraction becomes 90 , this angle of incidence is called critical angle (C). o When Angle of incidence exceeds the critical angle than light ray comes back in to the same medium after reflection from interface. This phenomenon is called Total internal reflection (TIR). r C >C 60 i 90° 2 2 1 O E3 Fig. 29.28 1 cosec C where (1) sin C (5) Field of vision of fish (or swimmer) : A fish (diver) inside the water can see the whole world through a cone with. Rarer Denser Fig. 29.30 r (2) Conditions for TIR (i) The ray must travel from denser medium to rarer medium. (3) Dependence of critical angle (a) R V C R C V (b) Sin C R D (a) Apex angle 2C 98 o (b) Radius of base r h tan C v R D D (for two media) D R v R D YG 1 (ii) Nature of the pair of media : Greater the refractive index lesser will be the critical angle. o (c) For (diamond-air) pair C di amond 24 o h 1 3h ; for water r 2 (c) Area of base A (a) For (glass- air) pair C glass 42 o (b) For (water-air) pair C water 49 Fig. 29.31 U (i) Colour of light (or wavelength of light) : Critical angle depends 1 upon wavelength as sin C >C C C ID (ii) The angle of incidence i must be greater than critical angle C C h 7 h 2 9 2 ; for water a h 2 7 ( 1) (6) Porro prism : A right angled isosceles prism, which is used in periscopes or binoculars. It is used to deviate light rays through 90 o and 180 o and also to erect the image. (iii) Temperature : With temperature rise refractive index of the material decreases therefore critical angle increases. 45 90o o 45o 45o U Common Examples of TIR 45o 45 45 o 90o (1) Looming : An optical illusion in cold countries o 45 o ST (2) Mirage : An optical illusion in deserts A B B A 90o 45 45 o o Fig. 29.32 Surface Refraction From Spherical (3) Brilliance of diamond : Fig. Due29.29 to repeated internal reflections diamond sparkles. (4) Optical fibre : Optical fibres consist of many long high quality composite glass/quartz fibres. Each fibre consists of a core and cladding. 1 O P I 1 2 O Fig. 29.33 P I 2 1642 Ray Optics (1) Refraction formula : 2 1 R 2 v 1 u Where 1 Refractive index of the medium from which light rays are coming (from object). (6) Principal focus : We define two principal focus for the lens. We are mainly concerned with the second principal focus (F). Thus wherever we write the focus, it means the second principal focus. First principal focus : An object point for which image is formed at infinity. 2 Refractive index of the medium in which light rays are entering. u = Distance of object, v = Distance of image, R = Radius of curvature F1 F1 (2) Lateral magnification : The lateral magnification m is the ratio of the image height to the object height h v or m i 1 h0 2 u (A) 60 1 2 P F2 hi u v Fig. 29.34 F2 E3 C h0 Lens (B) Second principal focus : An image point for an object at infinity. Fig. 29.37 (A) Focal Length, Power and Aperture of(B)Lens Fig. 29.38 (1) Focal length (f) : Distance of second principle focus from optical centre is called focal length ID (1) Lens is a transparent medium bounded by two refracting surfaces, such that at least one surface is curved. Curved surface can be spherical, cylindrical etc. (2) Lenses are of two basic types convex which are thicker in the middle than at the edges and concave for which the reverse holds. fconvex positive, fconcave negative, fplane (2) Aperture : Effective diameter of light transmitting area is called aperture. Intensityof image (Aperture)2 Biconcave U Plano convex Concavo convex D YG Biconvex (3) Power of lens (P) : Means the ability of a lens to deviate the path of the rays passing through it. If the lens converges the rays parallel to the principal axis its power is positive and if it diverges the rays it is negative. Plano concave Convexo concave (3) As there are two spherical surfaces, there are two centres of curvature C and C and correspondingly two radii of curvature R and R (4) The line joining C and CFig.is29.35 called the principal axis of the lens. The centre of the thin lens which is on the principal axis, is called the optical centre. (5) A ray passing through optical centre proceeds undeviated through the lens. 1 2 1 ST Incident light C2 R2 R1 R1 Positive R2 Negative C1 O R1 (A) R1 Negative R2 Positive Incident light C1 2 1 100 ; Unit of power is Diopter (D) f (m ) f (cm ) Pconvex positive, Pconcave negative, Pplane zero. Rules of Image Formation by Lens Convex lens : The image formed by convex lens depends on the position of object. (1) When object is placed at infinite (i.e. u = ) 2 U 1 Power of lens P C2 O R2 (B) Fig. 29.36 Image At F Real 2F F F Inverted Very small in size Magnification m 2f) Image Between F and 2F Real Inverted F 2F Very small in size Magnification m < – 1 (3) When object is placed at 2F (i.e. u = 2f Fig. ) 29.40 F 2F 2F Image At 2F F 2F F Fig. 29.41 2F Ray Optics 1643 Real Inverted Equal in size Magnification m = – 1 Lens Maker's Formula and Lens Formula (1) Lens maker's formula : If R and R are the radii of curvature of first and second refracting surfaces of a thin lens of focal length f and refractive index (w.r.t. surrounding medium) then the relation between f, , R and R is known as lens maker’s formula. 1 2 1 (4) When object is placed between F and 2F (i.e. f < u < 2f ) 2 1 1 1 ( 1) f R R 2 1 F 2F Table 29.3 : Focal length of different lenses Lens R1 R Fig. 29.42 fR E3 2F R1 F f ID R2 R R ( 1) f 2R Biconcave (6) When object is placed between F and optical center (i.e. u < f ) R1 R f R 2( 1) f R U R2 R D YG Plano-concave F 2F R1 f R2 R R ( 1) f 2 R F Fig. 29.44 (2) Lens formula : The expression which shows the relation between u, v and f is called lens formula. Concave lens : The image formed by a concave lens is always virtual, erect and diminished (like a convex mirror) U (1) When object is placed at ST R 2( 1) Plano-convex lens F Fig. 29.43 Image At F 2F Virtual Erect Point size Magnification m 1 For = 1.5 Focal length Biconvex lens (5) When object is placed at F (i.e. u = f ) At Real Inverted 2F Very large in size Magnification m >> – 1 60 Image Beyond 2F Real Inverted F 2F Large in size Magnification m > – 1 2F F 1 1 1 f v u Magnification The ratio of the size of the image to the size of object is called magnification. (1) Transverse magnification : m I v f f v O u f u f (use sign convention while solving the problem) Fig. 29.45 (2) When object is placed any where on the principal axis (2) Longitudinal magnification : m 2 2 Image Between optical centre and focus Virtual Erect Smaller in size F Magnification m < + 1 object m I v 2 v1 . For very small O u 2 u1 f f v dv v du u f u f 2 2 (3) Areal magnification : m s Ai f , m 2 Ao f u (A = Area of image, A = Area of object) i Fig. 29.46 o 1644 Ray Optics (4) Relation between object and image speed : If an object moves with constant speed (Vo ) towards a convex lens from infinity to focus, the image 2 f . Vo will move slower in the beginning and then faster. Also Vi f u Newton's Formula (2) Focal length of the lens f If the distance of object (x ) and image (x ) are not measured from optical centre, but from first and second principal foci then Newton's 1 D2 x 2 x 4D m1 m 2 2 formula states f x1 x 2 2 where m 1 I1 I ; m 2 2 and m 1 m 2 1. O O Cutting of Lens x1 x2 Fig. 29.47 Lens Immersed in a Liquid If a lens (made of glass) of refractive index is immersed in a liquid of refractive index , then its focal length in liquid, f is given by 1 1 1 ( l g 1) ......(i) fl R R 2 1 g l (2) A symmetric lens is cut along principle axis in two equal parts. Intensity of image formed by each part will be less compared as that of 1 complete lens.(aperture of each part is times that of complete lens). 2 Focal length remains same for each part. ID l E3 (1) A symmetric lens is cut along optical axis in two equal parts. Intensity of image formed by each part will be same as that of complete lens. Focal length is double the original for each part. F If fa is the focal length of lens in air, then 1 1 1 ( a g 1) fa R R 2 1 60 (3) Size of object O I1. I 2 F......(ii) f, P fl (a μ g 1) fa (l μ g 1) D YG f, P (2) If g l , then fl . It means lens behaves as a plane glass plate and becomes invisible in the medium. U f, P Combination of Lens Fig. 29.52 (1) For a system of lenses, the net power, net focal length and magnification are given as follows : P P1 P2 P3.......... , ST (2) In case when two thin lens are in contact : Combination will behave as a lens, which have more power or lesser focal length. Fig. 29.49 By this method focal length of convex lens is determined. Consider an object and a screen placed at a distance D (> 4f) apart. Let a lens of focal length f be placed between the object and the screen. x Object f2 I1 Screen P P1 P2 (4) When two lenses are placed co-axially at a distance d from each other then equivalent focal length (F). I2 D > 4f and (3) If two lens of equal focal length but of opposite nature are in contact then combination will behave as a plane glass plate and Fcombination f1 Fig. 29.50 1 1 1 1 ........... , F f1 f2 f3 m m 1 m 2 m 3 ............ f f 1 1 1 F 1 2 F f1 f2 f1 f2 O P/2 Fig. 29.51 That is the nature of lens remains unchanged, but it’s focal length increases and hence power of lens decreases. Displacement Method 2f (1) If g l , then fl and fa are of same sign and fl fa. (3) If g l , then fl and fa have opposite signs and the nature Fig. 29.48 of lens changes i.e. a convex lens diverges the light rays and concave lens converges the light rays. 2f P/2 U (1) For two different positions of lens two images (I1 and I 2 ) of an object are formed at the screen. d Fig. 29.53 Ray Optics 1645 Since fl R R R so F , fm 2 ( 1) 2 2 (2 1) Defects in Lens 1 1 1 d and P P1 P2 dP1 P2 F f1 f2 f1 f2 (1) Chromatic aberration : Image of a white object is coloured and blurred because (hence f) of lens is different for different colours. This defect is called chromatic aberration. (5) Combination of parts of a lens : 60 fV F=f F =f FR FV and f Violet Real White light fR Fig. 29.54 Fig. 29.59 F = f/2 E3 V R so fR fV and Mathematically chromatic aberration = f R fV ωf y = Dispersive power of lens. F= f f = Focal length for mean colour fR fV Fig. 29.55 y Silvering of Lens ID On silvering the surface of the lens it behaves as a mirror. The focal 1 2 1 length of the silvered lens is F fl fm Removal : To remove this defect i.e. for Achromatism we use two or more lenses in contact in place of single lens. 1 2 0 or Mathematically condition of Achromatism is : f1 f2 fm focal length of mirror from which reflection takes place. D YG (1) Plano convex is silvered F Marginal rays Paraxial ray + U R R R so F , fl ( 1) 2 2 ST F Marginal rays F F F Paraxial rays + Fig. 29.60 Removal : A simple method to reduce spherical aberration is to use a stop before and infront of the lens. (but this method reduces the intensity of the image as most of the light is cut off). Also by using plano-convex lens, using two lenses separated by distance d = F – F ', using crossed lens. (3) Coma : When the point object is placed away from the principle axis and the image is received on a screen perpendicular to the axis, the shape of the image is like a comet. This defect is called Coma. It refers to spreading of a point object in a plane to principle axis. fl Image of P fm Fig. 29.57 fm , fl F fm fl Fig. 29.56 fm 1 f2 2 f1 (2) Spherical aberration : Inability of a lens to form the point image of a point object on the axis is called Spherical aberration. In this defect all the rays passing through a lens are not focussed at a single point and the image of a point object on the axis is blurred. U where fl focal length of lens from which refraction takes place (twice) R R so F ( 1) 2 ( 1) P Axis (ii) Double convex lens is silvered P Removal : It can be reduced byFig. properly 29.61 designing radii of curvature of the lens surfaces. It can also be reduced by appropriate stops placed at appropriate distances from the lens. + (4) Curvature : For a point object placed off the axis, the image is spread both along and perpendicular to the principal axis. The best image fl F Fig. 29.58 fm 1646 Ray Optics is, in general, obtained not on a plane but on a curved surface. This defect is known as Curvature. Removal : Astigmatism or the curvature may be reduced by using proper stops placed at proper locations along the axis. (5) Distortion : When extended objects are imaged, different portions of the object are in general at different distances from the axis. The magnification is not the same for all portions of the extended object. As a result a line object is not imaged into a line but into a curve. (a) Refracted ray inside the prism is parallel to the base of the prism for equilateral and isosceles prisms. (b) r A 2 and i A m 2 A m 2 sin A / 2 sin (Prism formula). 60 sin i (c) or sin A / 2 (3) Condition of no emergence : For no emergence of light, TIR must takes place at the second surface (1) Refraction through a prism A r1 i – Angle of incidence, e – Angle of emergence, A – Angle of prism or refracting e angle of prism, r and r – Angle of refraction, – Angle of deviation r2 1 2 r 2 So, A 2C. incidence. for any angle 1 of r 2 TIR Fig. 29.66 If light ray incident normally on first surface i.e. i = 0° it means r = 0°. So in this case condition of no emergence from second surface is A > C. sin A sin C sin A 1 1 cosec A Dispersion Through a Prism D YG Fig. 29.63 1 The splitting of white light into it’s constituent colours is called dispersion of light. B C 1 U i i So A > r + C (From A = r + r ) ID Prism is a transparent medium bounded by refracting surfaces, such that the incident surface (on which light ray is incidenting) and emergent surface (from which light rays emerges) are plane and non parallel. A A 2 As maximum value of r1 C Fig. 29.62 Prism For TIR at second surface r > C E3 (6) Astigmatism : The spreading of image (of a point object placed Object Distorted away from the principal axis) along the principal axis isimages called Astigmatism. A r1 r2 and i e A For surface AC 1 sin r2 sin i ; For surface AB sin r1 sin e (2) Deviation through a prism : For thin prism ( 1)A. Also deviation is different for different colour light e.g. R V so R V. Flint Crown so F C U (i) Maximum deviation : Condition of maximum deviation is i 90 r1 C, r2 A C o ST and from Snell’s law on emergent surface i = 90 sin(A C) e sin1 sin C max V R Y max e r o Incident white light 2 r1 = C sin(A C) sin1 A 2 sinC r Fig. 29.64 R Y Fig. 29.68 (2) Dispersive power () : i e and R V y y 1 R wher e y V 2 It depends only upon the material of the prism i.e. and it doesn't depends upon angle of prism A e m i Fig. 29.65 Screen V r colours i.e. θ δ V δ R ( μ V μ R )A. It depends upon and A. (ii) Minimum deviation : It is observed if r1 r2 r , deviation produced is minimum. i Fig. 29.67 (1) Angular dispersion ( ) : Angular separation between extreme Ray Optics 1647 (3) Combination of prisms : Two prisms (made of crown and flint material) are combined to get either dispersion only or deviation only. (i) Dispersion without deviation (chromatic combination) Flint net R A V ' 1 ( ' ' ) Fig. 29.69 60 net Colour is defined as the sensation received by the eye (rod cells of the eye) due to light coming from an object. (i) A rose appears red in white light because it reflects red colour and absorbs all remaining colours. (ii) Deviation without dispersion (Achromatic combination) Flint (ii) When yellow light falls on a bunch of flowers, then yellow and white flowers looks yellow. Other flowers looks black. A (2) Colours of transparent object : The colours of transperent bodies are due to selective transmission.. R 1 ' Colours of Objects (1) Colours of opaque object : The colours of opaque bodies are due to selective reflection. e.g. Crown ( R ) A' V A ( ' V ' R ) arc is red and outermost is violet. (iii) It subtends an angle of 52.5 o at the eye. (iv) Comparatively less bright. V A (i) A red glass appears red because it absorbs all colours, except red which it transmits. Crown Fig. 29.70 (ii) When we look on objects through a green glass or green filter then green and white objects will appear green while other black. Scattering of Light (1) According to scientist Rayleigh : Intensity of scattered light 1 4 (4) Colour of clouds : Large particles like water droplets and dust do not have this selective scattering power. They scatter all wavelengths alomost equally. Hence clouds appear to the white. D YG U (2) Some phenomenon based on scattering : (i) Sky looks blue due to scattering. (iii) Danger signals are made of red colour. (3) Colour of the sky : Light of shorter wavelength is scattered much more than the light of longer wavelength. Since blue colour has relatively shorter wavelength, it predominates the sky and hence sky appears bluish. ID Molecules of a medium after absorbing incoming light radiations, emits them in all direction. This phenomenon is called Scattering. (ii) At the time of sunrise or sunset sun looks reddish. E3 ( y 1) A' A ( ' y 1) V R A (2) Secondary rainbow : (i) Two refraction and two TIR. (ii) Innermost (5) Colour triangle for spectral colours : Red, Green and blue are primary colours. Green (P) (3) Elastic scattering : When the wavelength of radiation remains unchanged, the scattering is called elastic. Cyan (S) (4) Inelastic scattering (Raman’s effect) : Under specific condition, light can also suffer inelastic scattering from molecules in which it’s wavelength changes. Rainbow U Rainbow is formed due to the dispersion of light suffering refraction and TIR in the droplets present in the atmosphere. Observer should stand with its back towards sun to observe rainbow. Yellow (S) white Red (P) Blue (P) Magenta (S) Fig. 29.72 (i) Complementary colours : Green and Magenta, Blue and Yellow, Red and Cyan. (ii) Combination : Green + Red + Blue = White, Blue + Yellow = White, Red + Cyan = White, Green + Magenta = White ST (6) Colour triangle for pigment and dyes : Red, Yellow and Blue are the primary colours. Yellow (P) Red Green (S) Violet Orange (S) Black 43o 41o 42o 40o 29.71 (1) Primary rainbow : (i) TwoFig.refraction and one TIR. (ii) Innermost arc is violet and outermost is red. (iii) Subtends an angle of 42 o at the eye of the observer. (iv) More bright Blue (P) Red (P) Radish violet (S) (Mauve) Fig. 29.73 (i) Complementary colours : Yellow and Mauve, Red and Green, Blue and Orange. 1648 Ray Optics (ii) Combination : Yellow + Red + Blue = Black, Blue + Orange = Black, Red + Green = Black, Yellow + Mauve = Black Spectrum The ordered arrangements of radiations according to wavelengths or frequencies is called Spectrum. Spectrum can be divided in two parts Emission spectrum and Absorption spectrum. the light emitted from the photosphere passes through the chromosphere, certain wavelengths are absorbed. Hence, in the spectrum of sunlight a large number of dark lines are seen called Fraunhoffer lines. Sun's atmosphere Cromosphere (1) Emission spectrum : When light emitted by a self luminous object is dispersed by a prism to get the spectrum, the spectrum is called emission spectra. Photosphere Fig. 29.77 (ii) It is produced by solids, liquids and highly compressed gases heated to high temperature. (ii) From the study of Fraunhoffer’s lines the presence of various elements in the sun’s atmosphere can be identified e.g. abundance of hydrogen and helium. (iii) In the event of a solar eclipse, dark lines become bright. This is because of the reason that the presence of an opaque obstacle in between sun and earth cuts the light off from the central region (photo-sphere), while light from corner portion (cromosphere) is still being received. The bright lines appear exactly at the places where dark lines were present. ID (iii) e.g. Light from the sun, filament of incandescent bulb, candle flame etc. (i) The prominent lines in the yellow part of the visible spectrum were labelled as D-lines, those in blue part as F-lines and in red part as C-line. E3 (i) It consists of continuously varying wavelengths in a definite wavelength range. 60 Continuous emission spectrum Fig. 29.74 (4) Spectrometer : A spectrometer is used for obtaining pure spectrum of a source in laboratory and calculation of of material of prism and of a transparent liquid. Line emission spectrum (i) It consist of distinct bright lines. (ii) It is produced by an excited source in atomic state. It consists of three parts : Collimator which provides a parallel beam of light; Prism Table for holding the prism and Telescope for observing the spectrum and making measurements on it. D YG U (iii) e.g. Spectrum of excited helium, mercury vapours, sodium vapours or atomic hydrogen. Band emission spectrum Fig. 29.75 The telescope is first set for parallel rays and then collimator is set for parallel rays. When prism is set in minimum deviation position, the spectrum seen is pure spectrum. Angle of prism (A) and angle of minimum deviation ( m ) are measured and of material of prism is calculated using prism formula. For of a transparent liquid, we take a hollow prism with thin glass sides. Fill it with the liquid and measure ( m ) and A of liquid (ii) It is produced by an excited source in molecular state. prism. of liquid is calculated using prism formula. (iii) e.g. Spectra of molecular H 2 , CO, NH 3 etc. (5) Direct vision spectroscope : It is an instrument used to observe pure spectrum. It produces dispersion without deviation with the help of n crown prisms and (n 1) flint prisms alternately arranged in a tabular structure. U (i) It consist of district bright bands. Fig. 29.76 ST (2) Absorption spectrum : When white light passes through a semitransparent solid, or liquid or gas, it’s spectrum contains certain dark lines or bands, such spectrum is called absorption spectrum (of the substance through which light is passed). For no deviation n ( 1)A (n 1) ( '1)A'. Human Eye (i) Substances in atomic state produces line absorption spectra. Polyatomic substances such as H 2 , CO 2 and KMnO4 produces band absorption spectrum. (ii) Absorption spectra of sodium vapour have two (yellow lines) wavelengths D1 (5890 Å) and D2 (5896 Å) (3) Fraunhoffer’s lines : The central part (photosphere) of the sun is very hot and emits all possible wavelengths of the visible light. However, the outer part (chromosphere) consists of vapours of different elements. When Fig. 29.78 (1) Eye lens : Over all behaves as a convex lens of 1.437 Ray Optics 1649 (2) Retina : Real and inverted image of an object, obtained at retina, brain sense it erect. (3) Yellow spot : It is the most sensitive part, the image formed at yellow spot is brightest. (5) Ciliary muscles : Eye lens is fixed between these muscles. It’s both radius of curvature can be changed by applying pressure on it through ciliary muscles. (6) Power of accomodation : The ability of eye to see near objects as well as far objects is called power of accomodation. (ii) In this defect focal length or radii of curvature of lens increases or power of lens decreases or distance between eye lens and retina decreases. (iii) This defect can be removed by using a convex lens. (iv) If a person cannot see before distance d but wants to see the dD object placed at distance D from eye so f and power of the lens dD 60 (4) Blind spot : Optic nerves goes to brain through blind spot. It is not sensitive for light. dD dD P A normal eye can see the objects clearly, only if they are at a distance greater than 25 cm. This distance is called Least distance of distinct vision and is represented by D. (3) Presbyopia : In this defect both near and far objects are not clearly visible. It is an old age disease and it is due to the loosing power of accommodation. It can be removed by using bifocal lens. (8) Persistence of vision : Is 1/10 sec. i.e. if time interval between two consecutive light pulses is lesser than 0.1 sec., eye cannot distinguish them separately. (4) Astigmatism : In this defect eye cannot see horizontal and vertical lines clearly, simultaneously. It is due to imperfect spherical nature of eye lens. This defect can be removed by using cylindrical lens (Torric lenses). (9) Binocular vision : The seeing with two eyes is called binocular vision. Lens Camera ID E3 (7) Range of vision : For healthy eye it is 25 cm (near point) to (far point). (10) Resolving limit : The minimum angular separation between two objects, so that they are just resolved is called resolving limit. For eye it is o 1 1' . 60 (1) In lens camera a converging lens of adjustable aperture is used. (2) Distance of film from lens is also adjustable. U (3) In photographing an object, the image is first focused on the film by adjusting the distance between lens and film. It is called focusing. After focusing, aperture is set to a specific value and then film is exposed to light for a given time through shutter. D YG Defects in Eye (1) Myopia (short sightness) : A short-sighted eye can see only nearer objects. Distant objects are not seen clearly. (4) f-number : The ratio of focal length to the aperture of lens is called f-number of the camera. (i) In this defect image is formed before the retina and Far point comes closer. 2, 2.8, 4, 5.6, 8, 11, 22, 32 are the f-numbers marked on aperture. Concave lens Retina Far point Retina d Focal length 1 Aperture f - number Aperture (5) Time of exposure : It is the time for which the shutter opens and light enters the camera to expose film. (i) If intensity of light is kept fixed then for proper exposure (B) Removal of Defect U (A) Defected eye f-number (ii) In this defect focal lengthFig.or29.79 radii of curvature of lens reduced or power of lens increases or distance between eye lens and retina increases. ST (iii) This defect can be removed by using a concave lens of suitable focal length. (iv) If defected far point is at a distance d from eye then Focal length of used lens f = – d = – (defected far point) (v) A person can see upto distance x, wants to see distance y xy x y (y > x) so f or power of the lens P x y xy (2) Hypermetropia (long sightness) : A long-sighted eye can see distant objects clearly but nearer object are not clearly visible. (i) Image formed behind the retina and near point moves away Retina I O Near point (A) Defected eye (B) Removal of Defect Fig. 29.80 1 (Aperture)2 (ii) If aperture is kept fixed then for proper exposure Time of exposure (t) 1 [Intensity(I)]2 I t constant I1t1 I2 t2 (iii) Smaller the f-number larger will be the aperture and lesser will be the time of exposure and faster will be the camera. (6) Depth of focus : It refers to the range of distance over which the object may lie so as to form a good quality image. Large f-number increase the depth of focus. Microscope Convex lens Retina Time of exposure (t) It is an optical instrument used to see very small objects. It’s magnifying power is given by 1650 Ray Optics Visual angle with instrument( ) Visual angle when object is placed at least distance of distinctvision( ) So v o ~ L D , the length of the tube. (1) Simple microscope (i) It is a single convex lens of lesser focal length. (ii) Also called magnifying glass or reading lens. Hence, we can write m D and m (iv) If lens is kept at a distance a from the eye then m D 1 and m (vii) Final image is formed at : Magnification mD D D and m m D 1 f max f min m ) D 1 fe Da f v0 D. and length of tube L v0 fe u0 fe In terms of length m Da f (L fo fe )D fo fe 60 (iii) Magnification’s, when final image is formed at D and (i.e. L fo (viii) For large magnification of the compound microscope, both fo and fe should be small. A (ix) If the length of the tube of microscope increases, then its magnifying power increases. Virtual and enlarged image E3 m (x) The magnifying power of the compound microscope may be expressed as M mo me ; where m is the magnification of the objective A o F B e ID B and m is magnifying power of eye piece. Astronomical Telescope (Refracting Type) ve=D to (2) Compound microscope vo fo A ue U uo By astronomical telescope heavenly bodies are seen. Fig. 29.81 ue B A D YG B Q B O B Q O A E A P ve=D to Fig. 29.83 ve=D to (1) fobjective feyelens and d objective d eye lens. Fig. 29.82 (i) Consist of two converging lenses called objective and eye lens. (2) Intermediate image is real, inverted and small. (ii) feye lens fobjective and (diameter) eye lens (diameter )objective (3) Final image is virtual, inverted and small. (iii) Intermediate image is real and enlarged. U (4) Magnification : m D (iv) Final image is magnified, virtual and inverted. ST ( A B ) formed by objective from objective, u e Distance of A B from eye Terrestrial Telescope lens, v = Distance of final image from eye lens, f = Focal length of objective, f = Focal length of eye lens. o f f0 f 1 e and m o fe D fe (5) Length : LD f0 ue and L f0 fe (v) u o Distance of object from objective (o), v o Distance of image e E It is used to see far off object on the earth. e v = D to e D 1 fe and length of the microscope tube (distance between two lenses) is LD v o ue. P v (vi) Final image is formed at D : Magnification m D o uo A A'' B Q B' O B'' Erecting lens A' Generally object is placed very near to the principal focus of the objective hence uo ~ fo. The eye piece is also of small focal length and the f o 2f 2f Fig. 29.84 image formed by the objective is also very near to the eye piece. U e (1) It consists of three converging lens : objective, eye lens and erecting lens. Ray Optics 1651 (2) It’s final image is virtual, erect and smaller. f0 fe (3) Magnification : m D R.L. f f 1 e and m 0 D fe P Q O E 1 resolving power (RP) aperture of objective. Fig. 29.85 If two telescopes are mounted parallel to each other so that an object can be seen by both the eyes simultaneously, the arrangement is called 'binocular'. In a binocular, the length of each tube is reduced by using a set of totally reflecting prisms which provide intense, erect image free from lateral inversion. Through a binocular we get two images of the same object from different angles at same time. Their superposition gives the perception of depth along with length and breadth, i.e., binocular vision gives proper three-dimensional (3D) image. ID f f 1 e and m 0 D fe (3) Length : L D f0 u e and L f0 fe Reflecting Telescope Reflecting telescopes are based upon the same principle except that the formation of images takes place by reflection instead of by refraction. fo U D YG T1 Light from 45o M T2 Objective 1 a 1 where a = R. P. d 1.22 E3 Binocular ue fo eye lens is diverging lens. (1) Objective is a converging lens while f 0 fe (2) Telescope : Smallest angular separations (d) between two distant objects, whose images are separated in the telescope is called resolving limit. 1.22 So resolving limit d a and A B Eye piece If f is focal length of the concave spherical mirror used as objective and f , the focal length of the eye-piece, the magnifying power of the Fig. 29.86 f reflecting telescope is given by m o fe o R. P. 60 ve=D to A U e = Half angle of the cone of light from the point object, sin = Numerical aperture. It is also type of terrestrial telescope but of much smaller field of view. (2) Magnification : m D 2 sin = Refractive index of the medium between object and objective, Galilean Telescope and R.P. = Wavelength of light used to illuminate the object, (4) Length : LD f0 4 f ue and L f0 4 f fe B 2 sin f e The branch of optics that deals with the study and measurement of Fig. 29.88 the light energy is called photometry. (1) Radiant flux (R) : The total energy radiated by a source per second is called radiant flux. It’s S.I. unit is Watt (W). (2) Luminous flux () : The total light energy emitted by a source per second is called luminous flux. It represents the total brightness producing capacity of the source. It’s S.I. unit is Lumen (lm). (3) Luminous efficiency () : The Ratio of luminous flux and radiant flux is called luminous efficiency i.e. . R Table 29.4 : Luminous flux and efficiency ST Further, if D is diameter of the objective and d, the diameter of the Photometry D2 pupil of the eye, then brightness ratio () is given by 2 d Light source 40 W tungsten bulb Resolving Limit and Resolving Power (1) Microscope : In reference to a microscope, the minimum distance between two lines at which they are just distinct is called Resolving limit (RL) and it’s reciprocal is called Resolving power ( RP) Flux (lumen) 465 Efficiency (lumen/watt) 12 60 W tungsten bulb 835 14 500 W tungsten bulb 9950 20 30 W fluorescent tube 1500 50 (4) Luminous Intensity (L) : In a given direction it is defined as luminous flux per unit solid angle i.e. O L Objective Fig. 29.87 Lightenergy lumen S.I. unit candela (Cd ) sec solid angle steradian 1652 Ray Optics The luminous intensity of a point source is given by : L 4 cos 4 (L) or I (5) Illuminance or intensity of illumination (I) : The luminous flux incident per unit area of a surface is called illuminance. I . It's S.I. A m 2 1 Phot 10 4 Lux or Lux (lx) and it's C.G.S. unit r3 i.e. I cos 3 or I 1 r3 (8) Photometer and Principle of Photometry : A photometer is a device used to compare the illuminance of two sources. L1 is Phot. L2 1 Lumen cm 2 60 Lumen Lh r1 (i) Intensity of illumination at a distance r from a point source is 1 I I 2. 4r 2 r (ii) Intensity of illumination at a distance r from a line source is 1 I I 2rl r (iii) In case of a parallel beam of light I r 0. r1 and r2 from the screen so that their flux are perpendicular to the screen. The distance L1 r12 and r1 r2 are adjusted till I1 I2. So L2 r22 L1 r1 L 2 r2 2 ; This is called principle of photometry. ID (iv) The illuminance represents the luminous flux incident on unit area of the surface, while luminance represents the luminous flux reflected from a unit area of the surface. r2 Fig. 29.92 L , and L are placed at distances Two sources of luminous intensity 1 2 E3 unit is h L so I 2 cos 3 r h After reflection velocity, wavelength and frequency of light remains same but intensity decreases. If light ray incident normally on a surface, after reflection it U (6) Relation Between Luminous Intensity (L) and Illuminance (I) : If S is a unidirectional point source of light of luminous intensity L and there is a surface at a distance r from source, on which light is falling normally. D YG (i) Illuminance of surface is given L by : I 2 r retraces the path. r S (ii) For a given source L = constant 1 so I 2 ; This is called. Inverse r square law of illuminance. Fig. 29.89 If two plane mirrors are inclined to each other at 90 , the emergent o ray is anti-parallel to incident ray, if it suffers one reflection from each. Whatever be the angle to incidence. We observe number of images in a thick plane mirror, out of them only second is brightest. Incident light (100%) U (7) Lambert’s Cosine Law of Illuminance : In the above discussion if surface is so oriented that light from the source falls, on it obliquely and the central ray of light makes an angle with the normal to the surface, then ST (i) Illuminance of the surface I L cos 10% r2 S C C 80% r Brightest image 9% To find the location of an object from an inclined plane mirror, you 0.9% have to see the perpendicular distance of the object from the mirror. Fig. 29.90 (ii) For a given light source and point of illumination (i.e. L and r = constant) I cos this is called Lambert’s cosine law of illuminance. L Io (at 0 o ) r2 (iii) For a given source and plane of illuminance (i.e. L and h = constant) S Imax I I O M Correct M Wrong O formed OM = MI Images by mirrors do not show chromatic aberration. OM = MI In concave mirror, minimum distance between a real object and it's real image is zero. (i.e. when u = v = 2f) h r If a spherical mirror produces an image ‘m’ times the size of the P P0 Fig. 29.91 Ray Optics 1653 object (m = magnification) then u, v and f are given by the followings m 1 m u f , v (m 1) f and f u m m 1 Number of images formed = Number of materials used Here no. of images = 5 Focal length of a mirror is independent of material of mirror and medium in which it is placed and wavelength of incident light Divergence or Convergence power of a mirror does not change with the change in medium. If an object is moving at a speed v towards a spherical mirror o along it’s axis then speed of image away from mirror is angle of incidence i min sin 1 2 1 sin A cos A . If a substance emits spectral lines at high temperature then it 2 .vo f When object is moved from focus to infinity at constant speed, the image will move faster in the beginning till object moves from f to 2f, and slower later on, towards the mirror. absorbs the same lines at low temperature. This is Kirchoff’s law. When a ray of white light passes through a glass prism red light is deviated less than blue light. 60 f vi u For the condition of grazing emergence through a prism. Minimum For a hollow prism A 0 but = 0 As every part of mirror forms a complete image, if a part of the O C If an opaque coloured object or crystal is crushed to fine powder it P I In case of refraction of light frequency (and hence colour) and phase do not change (while wavelength and velocity will change). In the refraction intensity of incident light decreases as it goes from one medium to another medium. will appear white (in sun light) as it will lose it's property of selective reflection. Our eye is most sensitive to that part of the spectrum which lies between the F line (sky green) and the C-line (red) of hydrogen, and the mean refractive index of this part is nearly equal to the refractive index for the D line (yellow) of sodium. Hence for the dispersive power, the C following formula is internationally accepted F D 1 ID F U A transparent solid is invisible in a liquid of same refractive index (Because of No refraction). When a glass slab is kept over various coloured letters and seen D YG from the top, the violet colour letters appears closer (Because v R so V R and from E3 mirror is obstructed, full image will be formed but intensity will be reduced. h h' Sometimes a part of prism is given and we keep on thinking whether how should we proceed ? To solve such problems first complete the prism then solve as the problems of prism are solved A if increases then h' decreases i.e. 50o Letter appears to be closer) Minimum distance between an object and it’s real image formed by a convex lens is 4f. Component lenses of an achromatic doublet cemented by canada blasam because it is transparent and has a refractive index almost equal to the refractive index of the glass. U Parabolic mirrors are free from spherical aberration. If a sphere of radius R made of material of refractive index 2 is placed in a medium of refractive index 1 , then if the object is placed at ST 1 R from the pole, the real image formed is a distance 2 1 equidistant from the sphere 1 1 O o o o 60 we look 70 When distant objects, the 60 eye is relaxed70 and it's focal o C B length is largest. Minimum separation (d) between objects, so they can just resolved r by a telescope is : d R.P. Where r = distance of objects from telescope. As magnifying power astronomical telescope is negative, the image seen in astronomical telescope is truly inverted, i.e., left is turned right with upside down simultaneously. However, as most of the astronomical objects are symmetrical this inversion does not affect the observations. If objective and eye lens of a telescope are interchanged, it will not behave as a microscope but object appears very small. In a telescope, if field and eye lenses are interchanged magnification P1 P2 I 2 will change from (f / f ) to (f / f ), i.e., it will change from m to (1/m), i.e., will become (1/m ) times of its initial value. As magnification produced by telescope for normal setting is (f / f ), so to have large magnification, f must be as large as practically possible and f small. This is why in a telescope, objective is of large focal length while eye piece of small. In a telescope, aperture of the field lens is made as large as practically possible to increase its resolving power as resolving power of a telescope (D/). Large aperture of objective also helps in improving o e e o 2 o x 2x x The lens doublets used in telescope are achromatic for blue and red colours, while these used in camera are achromatic for violet and green colours. The reason for this is that our eye is most sensitive between blue and red colours, while the photographic plates are most sensitive between violet and green colours. Composite lens : If a lens is made of several materials then 1 2 3 4 5 o e * e 1654 Ray Optics the brightness of image by gathering more light from distant object. However, it increases aberrations particularly spherical. For a telescope with increase in length of the tube, magnification decreases. In case of a telescope if object and final image are at infinity then : f D m o fe d d D fo fe 60 If we are given four convex lenses having focal lengths If a parrot is sitting on the objective of a large telescope and we look towards (or take a photograph)of distant astronomical object (say moon) through it, the parrot will not be seen but the intensity of the image will be slightly reduced as the parrot will act as obstruction to light and will reduce the aperture of the objective. monochromatic light of wavelength 5500 Å is called 1 lumen. RL R 1 1 L 1 R2 2 L2 ST U D YG (As = R = 4L) U While solving the problems of photometry keep in mind. ID The luminous flux of a source of (1/685) watt emitting E3 f1 f2 f3 f4. For making a good telescope and microscope. We choose the following lenses respectively. Telescope f1 (o), f4 (e ) Microscope f4 (o), f3 (e )
