Q.

Image formation from a thin prism: For a thin prism, at near normal incidence, the  angle of deviation does not vary considerably with angle of incidence and  consequently we may write angle of deviation as δ=(μ1)A, where A is the angle of the prism and μ is the refractive index of the material of the prism. Consider a thin  prism ABC and a source of light S. Suppose we want to trace the image of source S,  for sake of simplicity we draw a simple ray diagram as shown in the figure. Suppose we take S as the origin, S’ as the image of S and the horizontal and vertical  lines passing through S as x and y axis, and the distance SB as a (SB is  horizontal).Now using geometry and using the fact that angle CAB is small, we can  find the coordinates of S’.
Question Image     
Which of the following is/are correct? 

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a

Y coordinate of S’ will be (μ1)Aa

b

Y coordinate of S’ will be 2(μ1)Aa

c

X coordinate of S’ will be zero

d

X coordinate of S’ will be a/2

answer is A, C.

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Detailed Solution

Angle of deviation δ=(μ1)A,

Y=δa and X = 0

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Image formation from a thin prism: For a thin prism, at near normal incidence, the  angle of deviation does not vary considerably with angle of incidence and  consequently we may write angle of deviation as δ=(μ−1)A, where A is the angle of the prism and μ is the refractive index of the material of the prism. Consider a thin  prism ABC and a source of light S. Suppose we want to trace the image of source S,  for sake of simplicity we draw a simple ray diagram as shown in the figure. Suppose we take S as the origin, S’ as the image of S and the horizontal and vertical  lines passing through S as x and y axis, and the distance SB as a (SB is  horizontal).Now using geometry and using the fact that angle CAB is small, we can  find the coordinates of S’.     Which of the following is/are correct?