A ray of light is incident at an angle of 45∘ on a square slab of a transparent material. What should be the refractive index of the material of the slab so that the emergent ray travels along the vertical face AB?
Consider the refractive index of the slab to be x.
Light ray travels from medium 1 to medium 2.
By Snell's law,
sin isin r=Refractive index of medium 2Refractive index of medium 1
At the first interface
sin 45osin r=x1 ..(1)
At the second interface
⇒sin r=√x2−1x ..(2)
from (1) and (2)
1√2 × √x2−1x=x