A rectangular glass slab ABCD , of refractive index, n 1 , is immersed in water of refractive index n 2 ( n 1 n 2 ) . A ray of light is incident at the surface AB of the slab, as shown. The maximum

Question

A rectangular glass slab ABCD , of refractive index, n 1 , is immersed in water of refractive index n 2 ( n 1 > n 2 ) . A ray of light is incident at the surface AB of the slab, as shown. The maximum value of the angle of incidence α max , such that the ray comes out only from the other surface CD , is given by

TestHub · Accepted Answer

Consider the figure. The ray will come out from CD if it suffers a total internal reflection at surface AD , i.e., it strikes the surface AD at critical angle C (the limiting case). Applying Snell’s law at P , we get n 1 sin C = n 2 or sin C = n 2 n 1 Applying snell’s law at Q , we get n 2 sin α = n 1 cos C ; ⇒ sin α = n 1 n 2 cos { sin − 1 ( n 2 n 1 ) } or α = sin − 1 [ n 1 n 2 cos { sin − 1 ( n 2 n 1 ) } ]

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