Question

A ray of light, incident on an equilateral glass prism ( $bold italic mu subscript bold italic g equals square root of 3$ ) moves parallel to the base line of the prism inside it. Find the angle of incidence for this ray.

Solution

Since the prism is equilateral in shape,

Angle of prism, A = 60^o

Angle of refraction, r = A/2 = 30^o

Now, using Snell’s law,
$mu subscript g over mu subscript i equals fraction numerator sin space i over denominator sin space r end fraction$

$fraction numerator square root of 3 over denominator 1 end fraction equals fraction numerator sin space i over denominator sin space 30 degree end fraction$
$rightwards double arrow straight space sin straight space straight i straight space equals straight space fraction numerator square root of 3 over denominator 2 end fraction$
$i. e. comma space A n g l e space o f space i n c i d e n c e comma space i space equals space 60 degree$