physics refraction help please..

Question

A ray of the light incident on the slab of transparent material is partly reflected from the surface and partly refracted into the slab . The reflected rays are mutually perpendicular .The incident ray makes an angle i with the normal to the slab . The refractive index of the slab is?

 

1. tan ^-1  (i)
2. cot^-1  (i)
3. sin^-1  (i)
4.  cos^-1  (i)

Answer 1

 

 

n1 sin theta1 = n2 sin theta2

 

n1 = 1 (assumed)

 

Assuming reflected and refracted rays are perpendicular,

 

incident ray at i wrt normal

reflected ray must be at angle i wrt normal

i + pi/2 is refracted ray's angle wrt outer normal

refracted angle is pi - (i + pi/2) = pi/2-i

 

n2 = sin i / sin (pi/2 - i)

 

sin(pi/2 - i) = sin pi/2 cos (i) - cos(pi/2) sin i = cos i

 

n2 = sin i / cos i = tan i

 

index of refraction of the slab is tan(i).