Eduprobe
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?
l is dependent on n(z)
n1sinθ1=(n2−n1)sinθf
l is independent of n2
n1sinθi=n2sinθf
Solution:
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.