PhysicsA 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?

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?

  1. A

    l is dependent on n(z)

  2. B

    n1sinθi=n2n1sinθf

  3. C

    n1sinθi=n2sinθf

  4. D

    l is independent of n2

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    Solution:

    Since refraction occurs at a set of parallel surfaces,  n1sinθi=n2sinθf
    The lateral displacement will depend on how the n(z) varies in the medium . 

    Clearly, l does not depend on n.

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