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Q.

A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and  n2 (>n1) , as shown in the figure. A ray of light is incident with angle  θi from medium 1 and emerges in medium 2 with refraction angle θf  with a lateral displacement l.Which of the following statement (s) is (are) true?

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a

l is dependent on n(z)

b

n1 sinθi= n2 sinθf

c

n1 sinθi= (n2−n1) sinθf

d

l is independent of n2

answer is A.

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Detailed Solution

Snell's Law , n1 sinθi= n2 sinθfLateral displacement occurs before the light emerges out in medium n2 . Hence it does not depend on medium 2.Lateral displacement depends on θi , n1 , n(z)
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A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and  n2 (>n1) , as shown in the figure. A ray of light is incident with angle  θi from medium 1 and emerges in medium 2 with refraction angle θf  with a lateral displacement l.Which of the following statement (s) is (are) true?