For the given incident ray as shown in the figure, for total internal reflection of this ray, the required refractive index of the prism will be [figure]
(3) 32
At the top face i = 45 , so by Snell's law
45 = r
r = 1 2
The faces are perpendicular, so the angle of incidence on the side face is (90 - r), and for total internal reflection there
(90 - r) 1
r 1
1 - 12 2 1 2
2 32
∴ = 32 (minimum required value)
Answer: (3)
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