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  4. A ray of light is incident normally on one face of a right angled isosceles prism. It then grazes the hypotenuse. The refractive index of the material of the prism is

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Q. A ray of light is incident normally on one face of a right angled isosceles prism. It then grazes the hypotenuse. The refractive index of the material of the prism is

KCETKCET 2007Ray Optics and Optical Instruments

Solution:

Refractive index, $\mu = \frac{1}{sin C'}$
where C is the critical angle.
image
Here, $C = 45^{\circ}$ (as shown) $ \mu = \frac{1}{sin 45 ^{\circ}}$
or $\mu = \sqrt{2} $
or $ \mu = 1.414$