Reflection and Refraction - Science Textbook

 i. The angle of incidence is equal to the angle of reflection, and ii. The incident ray, the normal to the mirror at the point of incidence and the reflected ray, all lie in the same plane. SPHERICAL MIRRORS ================= +-----------------------+------------------...

 i. The angle of incidence is equal to the angle of reflection, and ii. The incident ray, the normal to the mirror at the point of incidence and the reflected ray, all lie in the same plane. SPHERICAL MIRRORS ================= +-----------------------+-----------------------+-----------------------+ | - - - - | | | +-----------------------+-----------------------+-----------------------+ Science Image Formation by Spherical Mirrors ------------------------------------ +-----------------------+-----------------------+-----------------------+ | - - - - | | | | | | | | | | | | | | | | - - | | | | | | | | | | | | | | | | - - | | | +-----------------------+-----------------------+-----------------------+ -- -- -- -- -- -- -- -- Representation of Images Formed by Spherical Mirrors Using Ray Diagrams ----------------------------------------------------------------------- a. b. i. *A ray parallel to the principal axis*, after reflection, will pass through the principal focus in case of a concave mirror or appear to diverge from the principal focus in case of a convex mirror. This is illustrated in Fig.9.3 a. and (b). Science ii. *A ray passing through the principal focus* of a concave mirror or *a ray which is directed towards the principal focus of* a convex mirror, after reflection, will emerge parallel to the principal axis. This is illustrated in Fig.9.4 (a) and (b). iii. *A ray passing through the centre of curvature* of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path. This is illustrated in Fig.9.5 (a) and *Figure 9.4* *(a)* iv. *A ray incident obliquely to the principal axis*, towards a point P (pole of the mirror), on the concave mirror \[Fig. 9.6 (a)\] or a convex mirror \[Fig. 9.6 (b)\], is reflected obliquely. The incident and reflected rays follow the laws of reflection at the point of incidence (point P), making equal *Figure 9.6* ### Image formation by Concave Mirror   +-----------------------+-----------------------+-----------------------+ | - - - - - | | | +-----------------------+-----------------------+-----------------------+ ### Uses of concave mirrors ### Image formation by a Convex Mirror Science +-----------------------+-----------------------+-----------------------+ | - - - - - | | | +-----------------------+-----------------------+-----------------------+  -- -- -- -- -- -- -- -- +-----------------------+-----------------------+-----------------------+ | - - | | | +-----------------------+-----------------------+-----------------------+ ### Uses of convex mirrors Sign Convention for Reflection by Spherical Mirrors --------------------------------------------------- i. The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side. ii. All distances parallel to the principal axis are measured from the pole of the mirror. iii. All the distances measured to the right of the origin (along iv. Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive. v. Distances measured perpendicular to and below the principal axis (along --y-axis) are taken as negative. Science Mirror Formula and Magnification -------------------------------- ### Magnification *h* ′ *m* = *h* ### Example 9.1 ### Solution *v u f* or, = [ 1] − *v f u* *v* = = + 1.15 m *h u* = + 0.23 ### Example 9.2 ### Solution *v u f* or, = [ 1] *v f u* Science REFRACTION OF LIGHT =================== +-----------------------+-----------------------+-----------------------+ | - - - - | | | +-----------------------+-----------------------+-----------------------+ +-----------------------+-----------------------+-----------------------+ | - - - - | | | +-----------------------+-----------------------+-----------------------+ +-----------------------+-----------------------+-----------------------+ | - - - - - | | | +-----------------------+-----------------------+-----------------------+ Refraction through a Rectangular Glass Slab ------------------------------------------- Science +-----------------------+-----------------------+-----------------------+ | - - - - - - | | | | - - - | | | +-----------------------+-----------------------+-----------------------+ vi. *The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.* vii. *The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media.* This law is also known as Snell's law of refraction. (This is true for angle 0 \< *i* \< 90^o^) The Refractive Index -------------------- 2 = Speed of light in medium 2 Speed of light in medium 1 Science +-----------------+-----------------+-----------------+-----------------+ | | 1.0003 | | | | | | | | | | 1.31 | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ Refraction by Spherical Lenses ------------------------------ Science +-----------------------+-----------------------+-----------------------+ | - - - | | | +-----------------------+-----------------------+-----------------------+ Image Formation by Lenses ------------------------- +-----------------------+-----------------------+-----------------------+ | - - - - - | | | | | | | | | | | | | | | | - - | | | +-----------------------+-----------------------+-----------------------+ Science +-----------------------+-----------------------+-----------------------+ | - - - - - | | | +-----------------------+-----------------------+-----------------------+ -- -- -- -- -- -- -- -- Image Formation in Lenses Using Ray Diagrams -------------------------------------------- viii. A ray of light from the object, parallel to the principal axis, after refraction from a convex lens, passes through the principal focus on the other side of the lens, as shown in Fig. 9.13 (a). In case of a concave lens, *Figure 9.13* *(a)* *(a)* *(b)* *(b)* ix. A ray of light passing through a principal focus, after refraction from a convex lens, will emerge parallel to the principal axis. This is shown in Fig. 9.14 (a). A ray of light appearing to meet at the principal focus of a concave lens, after refraction, will emerge parallel to the principal axis. This is shown in Fig.9.14 (b). x. A ray of light passing through the optical centre of a lens will emerge without any deviation. This is illustrated in Fig.9.15(a) and Fig.9.15 (b).  Science  Sign Convention for Spherical Lenses ------------------------------------ Lens Formula and Magnification ------------------------------ ### Magnification ### Example 9.3 ### Solution *v u f* 1 = 1 -- *u* --10 − 30 cm 3 ### Example 9.4 Science ### Solution 1 = 1 Power of a Lens --------------- Science - Mirror formula, *+* *=* [ 1] , gives the relationship between the object-distance (*u*), - The focal length of a spherical mirror is equal to half its radius of curvature. - The magnification produced by a spherical mirror is the ratio of the height of the image to the height of the object. - A light ray travelling obliquely from a denser medium to a rarer medium bends away from the normal. A light ray bends towards the normal when it travels obliquely from a rarer to a denser medium. - Light travels in vacuum with an enormous speed of 3×10^8^ m s^-1^. The speed of light is different in different media. - The refractive index of a transparent medium is the ratio of the speed of light in vacuum to that in the medium. - In case of a rectangular glass slab, the refraction takes place at both air-glass interface and glass-air interface. The emergent ray is parallel to the direction of incident ray. - Lens formula, *--* *=* [ 1] , gives the relationship between the object-distance (*u*), - Power of a lens is the reciprocal of its focal length. The SI unit of power of a lens is c. the mirror is concave and the lens is convex. d. the mirror is convex, but the lens is concave. 5. No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be a. only plane. b. only concave. c. only convex. d. either plane or convex. 6. Which of the following lenses would you prefer to use while reading small letters found in a dictionary? e. A convex lens of focal length 50 cm. f. A concave lens of focal length 50 cm. g. A convex lens of focal length 5 cm. h. A concave lens of focal length 5 cm. 7. We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case. 8. Name the type of mirror used in the following situations. i. Headlights of a car. j. Side/rear-view mirror of a vehicle. k. Solar furnace. 9. One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations. 10. An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed. 11. A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram. 12. An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image. 13. The magnification produced by a plane mirror is +1. What does this mean? 14. An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size. 15. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image. 16. Find the focal length of a lens of power -- 2.0 D. What type of lens is this? 17. A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging? Science