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Page 2 Differentiating w.r.t time , we get v (im)x = v (om)x ; v (im)y = v (om)y ; v (im)z = v (om)z , 3. Spherical Mirror 1 v + 1 u = 2 R = 1 f ..... Mirror formula x co–ordinate of centre of Curvature and focus of Concave mirror are negative and those for Convex mirror are positive. In case of mirrors since light rays reflect back in  X direction, therefore ve sign of v indicates real image and +ve sign of v indicates virtual image (b) Lateral magnification (or transverse magnification) m= h h 2 1 m = ? v u . (d) On differentiating (a) we get dv du = ? v u 2 2 . (e) On differentiating (a) with respect to time we get dv dt v u du dt ? ? 2 2 ,where dv dt is the velocity of image along Principal axis and du dt is the velocity of object along Principal axis. Negative sign implies that the image , in case of mirror, always moves in the direction opposite to that of object.This discussion is for velocity with respect to mirror and along the x axis. (f) Newton's Formula: XY = f 2 X and Y are the distances ( along the principal axis ) of the object and image respectively from the principal focus. This formula can be used when the distances are mentioned or asked from the focus. (g) Optical power of a mirror (in Diopters) = f 1 f = focal length with sign and in meters. (h) If object lying along the principal axis is not of very small size, the longitudinal magnification = 1 2 1 2 u u v v ? ? (it will always be inverted) Page 3 Differentiating w.r.t time , we get v (im)x = v (om)x ; v (im)y = v (om)y ; v (im)z = v (om)z , 3. Spherical Mirror 1 v + 1 u = 2 R = 1 f ..... Mirror formula x co–ordinate of centre of Curvature and focus of Concave mirror are negative and those for Convex mirror are positive. In case of mirrors since light rays reflect back in  X direction, therefore ve sign of v indicates real image and +ve sign of v indicates virtual image (b) Lateral magnification (or transverse magnification) m= h h 2 1 m = ? v u . (d) On differentiating (a) we get dv du = ? v u 2 2 . (e) On differentiating (a) with respect to time we get dv dt v u du dt ? ? 2 2 ,where dv dt is the velocity of image along Principal axis and du dt is the velocity of object along Principal axis. Negative sign implies that the image , in case of mirror, always moves in the direction opposite to that of object.This discussion is for velocity with respect to mirror and along the x axis. (f) Newton's Formula: XY = f 2 X and Y are the distances ( along the principal axis ) of the object and image respectively from the principal focus. This formula can be used when the distances are mentioned or asked from the focus. (g) Optical power of a mirror (in Diopters) = f 1 f = focal length with sign and in meters. (h) If object lying along the principal axis is not of very small size, the longitudinal magnification = 1 2 1 2 u u v v ? ? (it will always be inverted) 4. Refraction of Light vacuum. ? ? ? speed of light in vacuum speed of light in medium c v . 4.1 Laws of Refraction (at any Refracting Surface) (b) r Sin i Sin = Constant for any pair of media and for light of a given wave length. This is known as Snell's Law. More precisely, Sin i Sin r = n n 2 1 = v v 1 2 = ? ? 1 2 4.2 Deviation of a Ray Due to Refraction Deviation ( ?) of ray incident at ? ?i and refracted at ? ?r is given by ? = i ? r. 5. Principle of Reversibility of Light Rays A ray travelling along the path of the reflected ray is reflected along the path of the incident ray. A refracted ray reversed to travel back along its path will get refracted along the path of the incident ray. Thus the incident and refracted rays are mutually reversible. 7. Apparent Depth and shift of Submerged Object At near normal incidence (small angle of incidence i) apparent depth (d ?) is given by: d ?= relative n d ? n relative = ) refraction of medium of . I . R ( n ) incidence of medium of . I . R ( n r i Apparent shift = d ? ? ? ? ? ? ? ? ? rel n 1 1 Refraction through a Composite Slab (or Refraction through a number of parallel media, as seen from a medium of R. I. n 0 ) Apparent depth (distance of final image from final surface) = t n rel 1 1 + t n rel 2 2 + t n rel 3 3 +......... + rel n n n t Page 4 Differentiating w.r.t time , we get v (im)x = v (om)x ; v (im)y = v (om)y ; v (im)z = v (om)z , 3. Spherical Mirror 1 v + 1 u = 2 R = 1 f ..... Mirror formula x co–ordinate of centre of Curvature and focus of Concave mirror are negative and those for Convex mirror are positive. In case of mirrors since light rays reflect back in  X direction, therefore ve sign of v indicates real image and +ve sign of v indicates virtual image (b) Lateral magnification (or transverse magnification) m= h h 2 1 m = ? v u . (d) On differentiating (a) we get dv du = ? v u 2 2 . (e) On differentiating (a) with respect to time we get dv dt v u du dt ? ? 2 2 ,where dv dt is the velocity of image along Principal axis and du dt is the velocity of object along Principal axis. Negative sign implies that the image , in case of mirror, always moves in the direction opposite to that of object.This discussion is for velocity with respect to mirror and along the x axis. (f) Newton's Formula: XY = f 2 X and Y are the distances ( along the principal axis ) of the object and image respectively from the principal focus. This formula can be used when the distances are mentioned or asked from the focus. (g) Optical power of a mirror (in Diopters) = f 1 f = focal length with sign and in meters. (h) If object lying along the principal axis is not of very small size, the longitudinal magnification = 1 2 1 2 u u v v ? ? (it will always be inverted) 4. Refraction of Light vacuum. ? ? ? speed of light in vacuum speed of light in medium c v . 4.1 Laws of Refraction (at any Refracting Surface) (b) r Sin i Sin = Constant for any pair of media and for light of a given wave length. This is known as Snell's Law. More precisely, Sin i Sin r = n n 2 1 = v v 1 2 = ? ? 1 2 4.2 Deviation of a Ray Due to Refraction Deviation ( ?) of ray incident at ? ?i and refracted at ? ?r is given by ? = i ? r. 5. Principle of Reversibility of Light Rays A ray travelling along the path of the reflected ray is reflected along the path of the incident ray. A refracted ray reversed to travel back along its path will get refracted along the path of the incident ray. Thus the incident and refracted rays are mutually reversible. 7. Apparent Depth and shift of Submerged Object At near normal incidence (small angle of incidence i) apparent depth (d ?) is given by: d ?= relative n d ? n relative = ) refraction of medium of . I . R ( n ) incidence of medium of . I . R ( n r i Apparent shift = d ? ? ? ? ? ? ? ? ? rel n 1 1 Refraction through a Composite Slab (or Refraction through a number of parallel media, as seen from a medium of R. I. n 0 ) Apparent depth (distance of final image from final surface) = t n rel 1 1 + t n rel 2 2 + t n rel 3 3 +......... + rel n n n t Apparent shift = t 1 ? ? ? ? ? ? ? ? ? rel 1 n 1 1 + t 2 ? ? ? ? ? ? ? ? ? rel 2 n 1 1 +........+ ? ? ? ? ? ? ? ? ? rel n n n 1 8. Critical Angle and Total Internal Reflection ( T. I. R.) ?C = sin ?1 n n r d (i) Conditions of T. I. R. (a) light is incident on the interface from denser medium. (b) Angle of incidence should be greater than the critical angle (i > c). 9. Refraction Through Prism 9.1 Characteristics of a prism ? = (i + e) ? (r 1 + r 2 ) and r 1 + r 2 = A ? ? ? ? ? ? = i + e ? A. 9.2 Variation of ? versus i Page 5 Differentiating w.r.t time , we get v (im)x = v (om)x ; v (im)y = v (om)y ; v (im)z = v (om)z , 3. Spherical Mirror 1 v + 1 u = 2 R = 1 f ..... Mirror formula x co–ordinate of centre of Curvature and focus of Concave mirror are negative and those for Convex mirror are positive. In case of mirrors since light rays reflect back in  X direction, therefore ve sign of v indicates real image and +ve sign of v indicates virtual image (b) Lateral magnification (or transverse magnification) m= h h 2 1 m = ? v u . (d) On differentiating (a) we get dv du = ? v u 2 2 . (e) On differentiating (a) with respect to time we get dv dt v u du dt ? ? 2 2 ,where dv dt is the velocity of image along Principal axis and du dt is the velocity of object along Principal axis. Negative sign implies that the image , in case of mirror, always moves in the direction opposite to that of object.This discussion is for velocity with respect to mirror and along the x axis. (f) Newton's Formula: XY = f 2 X and Y are the distances ( along the principal axis ) of the object and image respectively from the principal focus. This formula can be used when the distances are mentioned or asked from the focus. (g) Optical power of a mirror (in Diopters) = f 1 f = focal length with sign and in meters. (h) If object lying along the principal axis is not of very small size, the longitudinal magnification = 1 2 1 2 u u v v ? ? (it will always be inverted) 4. Refraction of Light vacuum. ? ? ? speed of light in vacuum speed of light in medium c v . 4.1 Laws of Refraction (at any Refracting Surface) (b) r Sin i Sin = Constant for any pair of media and for light of a given wave length. This is known as Snell's Law. More precisely, Sin i Sin r = n n 2 1 = v v 1 2 = ? ? 1 2 4.2 Deviation of a Ray Due to Refraction Deviation ( ?) of ray incident at ? ?i and refracted at ? ?r is given by ? = i ? r. 5. Principle of Reversibility of Light Rays A ray travelling along the path of the reflected ray is reflected along the path of the incident ray. A refracted ray reversed to travel back along its path will get refracted along the path of the incident ray. Thus the incident and refracted rays are mutually reversible. 7. Apparent Depth and shift of Submerged Object At near normal incidence (small angle of incidence i) apparent depth (d ?) is given by: d ?= relative n d ? n relative = ) refraction of medium of . I . R ( n ) incidence of medium of . I . R ( n r i Apparent shift = d ? ? ? ? ? ? ? ? ? rel n 1 1 Refraction through a Composite Slab (or Refraction through a number of parallel media, as seen from a medium of R. I. n 0 ) Apparent depth (distance of final image from final surface) = t n rel 1 1 + t n rel 2 2 + t n rel 3 3 +......... + rel n n n t Apparent shift = t 1 ? ? ? ? ? ? ? ? ? rel 1 n 1 1 + t 2 ? ? ? ? ? ? ? ? ? rel 2 n 1 1 +........+ ? ? ? ? ? ? ? ? ? rel n n n 1 8. Critical Angle and Total Internal Reflection ( T. I. R.) ?C = sin ?1 n n r d (i) Conditions of T. I. R. (a) light is incident on the interface from denser medium. (b) Angle of incidence should be greater than the critical angle (i > c). 9. Refraction Through Prism 9.1 Characteristics of a prism ? = (i + e) ? (r 1 + r 2 ) and r 1 + r 2 = A ? ? ? ? ? ? = i + e ? A. 9.2 Variation of ? versus i (1) There is one and only one angle of incidence for which the angle of deviation is minimum. (2) When ? = ? min , the angle of minimum deviation, then i = e and r 1 = r 2 , the ray passes symmetrically w.r.t. the refracting surfaces. We can show by simple calculation that ? min = 2i min – A where i min = angle of incidence for minimum deviation and r = A/2. ? n rel = ? ? ? ? 2 A 2 A sin sin m ? ? , where n rel = n n prism surroundings Also ? ? ? ? ? ? min = (n ? 1) A (for small values of ? A) (3) For a thin prism ( A ?10 o ) and for small value of i, all values of ? ? ? = ( n rel ? 1 ) A where n rel = g surroundin prism n n 10. Dispersion Of Light The angular splitting of a ray of white light into a number of components and spreading in different directions is called Dispersion of Light. This phenomenon is because waves of different wavelength move with same speed in vacuum but with different speeds in a medium. The refractive index of a medium depends slightly on wavelength also. This variation of refractive index with wavelength is given by Cauchy’s formula. Cauchy's formula n ( ?) =a b ? ? 2 where a and b are positive constants of a medium. Angle between the rays of the extreme colours in the refracted (dispersed) light is called angle of dispersion. For prism of small ‘A’ and with small ‘i’ : ? = (n v – n r )A Deviation of beam(also called mean deviation) ? = ? y = (n y – 1)A Dispersive power ( ?) of the medium of the material of prism is given by: ? = 1 n n n y r v ? ? For small angled prism ( A ?10 o ) with light incident at small angle i : 1 n n n y r v ? ? = y r v ? ? ? ? = y ? ? = angular dispersion deviation of mean ray yellow ( )Read More
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1. What is the formula for magnification in the context of ray optics? 
2. How can one determine the focal length of a lens using ray optics? 
3. What is the difference between a real image and a virtual image in ray optics? 
4. How does total internal reflection occur in optical instruments? 
5. How can the power of a lens be calculated in the context of optical instruments? 

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