A beam of light enters the short side of a right-triangular prism that hasangles

Question

A beam of light enters the short side of a right-triangular prism that hasangles of 30º and 60º, as shown. The light totally internally reflects from thehypotenuse, then exits through the other side. There is air outside the prism.

a) What is the minimum index of refraction that the prism material can have toproduce total internal reflection from the hypotenuse in this setup? ANSWER: 1.15

(b)Now suppose you know that the prism is made of glass with  = 1.52 . When the beam leaves
the prism, what angle (in degrees) will it make with the surface normal (dashed line)? ANSWER:49.4°

Explanation / Answer

here,

(a)

the angle of incidence at the hypotnuse , i = 60 degree

let the refractive index of the prism be n

using snell's law

n = 1/(sin(60))

n = 1.15

for total internal refraction , the minimum refractive index of the prism is 1.15

(b)

when angle of incidence i' = (90 - 60)

i' = 30 degree

n = 1.52

let the angle of refraction at the perpendicular be r'

using snell's law

sin(r') /sin( i') = 1.52

r' = 49.4 degree

the angle it will make with the surface normal is 49.4 degree

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