A ray of light incident on one face of equilateral glass prism is refracted in such a way that it emerges from opposite surface at an angle of 90 to the normal. Calculate the angle of incidence

i ≅

Explanation:

Let the angle of incidence be represented by i, angle of emergence be represented by e, and angle of refraction by r.

Snell's law states that;

n = ................ 1

where n is the refractive index of the prism.

Given that emergence =

But from a ray diagram for the given question, we have;

+ ( - r) + ( - ) = (sum of angles in a triangle) .................. 2

( - r ) + ( - ) =   -

180° - (r + ) =   -

r +  =

⇒  r = -  ........................ 3

The refractive index of the equilateral prism = 1.5.

Applying Snell's law to the refracting surface,

  =

=

⇒    =

From equation 3,

r = -

r = -

r =

So that ;

n =

1.5 =

sin i = 0.4683

i = ≅