Question

A glass prism has n=1.5 and refracting angle is 90°.if a ray falls on it at angle of incidence of 30°,then the angle of emergence is

Answer 1

The relationship between critical angle and refractive index can be mathematically written as:

sin C = $\frac{1}{u}$

where C is critical angle and u is refractive index of the medium

We know that above critical angle there is total internal reflection

Lets find C for the question using above formula to check if any internal refraction is not happening.

So C = $sin^{-1}(\frac{1}{u} )$

C = $sin^{-1}(\frac{1}{1.5} )$

C = $sin^{-1}(0.667)$

C = 41.8 degrees

i = 30 degrees

i is angle of incidence and r is angle of refraction

we know $\frac{sin(i)}{sin(r)} = \frac{1}{u}$

$\frac{sin(30)}{sin(r)} = \frac{1}{1.5}$

sin r  = 1.5 x sin(30)

sin r = 1.5 x 0.5

sin r = 0.75

r = $sin^{-1}$(0.75)

r = 48.59 degrees