Question

# 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 incident with angle θi from medium 1 and emerges in medium 2 with refraction angle θf with lateral displacement l.Which of the following statement(s) is (are) true? A
l is dependent on n(z)
B
n1sinθ1=(n2n1)sinθf
C
n1sinθi=n2sinθf
D
l is independent of n2
Solution
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#### n1sinθi=n2sinθf since law of refraction is valid at each boundary.l is independent of n2 since the lateral displacement occurs even before the light enters medium 2.l is dependent on n(z) since lateral displacement depends on the refractive index.Answer is A,C and D.

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