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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 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?
478123.png
  1. n1sinθ1=(n2n1)sinθf
  2. n1sinθi=n2sinθf
  3. l is independent of n2
  4. l is dependent on n(z)

A
l is dependent on n(z)
B
n1sinθi=n2sinθf
C
n1sinθ1=(n2n1)sinθf
D
l is independent of n2
Solution
Verified by Toppr

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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