A wide slab consisting of two media of refractive indices n 1 and n 2 is placed in air as shown in the figure. A ray of light is incident from medium n 1 to n 2 at an angle θ , where sin θ is slightly larger than 1 n 1 . Take refractive index of air as 1 . Which of the following statement(s) is (are) correct?
D. The light ray is reflected back into the medium of refractive index n 1 if n 2 = 1 .
Option A: If n 1 = n 2 , n 1 sin θ = n 2 sin θ 1             . . . 1 and n 2 sin θ 1 = 1 × sin r           . . . 2 From (1) and (2), sin r = n 1 sin θ Now, sin θ > 1 n 1 , (given) ∴   sin r > 1 (which is not possible) and hence light will reflect back from air ,   n 2 interface Option B: If n 2 < n 1 , Snell's law at A , n 1 sin θ = n 2 sin θ 1           . . . 3 Snell's law at B n 2 sin θ 1 = sin r       . . . ( 4 ) From 3   and   ( 4 ) , n 1 sin θ = sin r ∴     sin r > 1 (not possible) Hence, light might reflect from A or B . Option C: If n 2 > n 1 , n 1 sin θ = n 2 sin θ 1               . . . 5 at A n 2 sin θ = 1 × sin r               . . . 6 at B ∴     n 1 sin θ = 1 × sin r ∴ sin r > 1 (not possible) ∴ Light will reflect back into medium n 1 . Option D: If n 2 = 1 , n 1 sin θ = n 2 sin θ 1 ⇒ sin θ 1 = n 1 sin θ or sin θ 1 > 1 not possible Hence, light will reflect back into the medium.
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