Question

How to prove that incident ray is parallel to emergent ray in refraction?

Answer 1

By using snell's law of refraction we can prove it.
n21 = Sin i/Sin r

n21 = 1/n12
n12 = Sin r/Sin e

n21 = sin e / sinr
sin i / sinr = sin e/ sin r
thus , Sin i = Sin e
therefore , Incident ray is parallel to emergent ray

Answer 2

An incident ray is parallel to emergent ray in refraction as the angle of incidence is equal to the angle of emergence.

Let the refractive index of the medium be = u

Snell's law is a theory used to describe the relationship between incidence and refraction angles when referring to light or other waves crossing a boundary between two separate isotropic mediums, such as water, glass or air.

According to snell's law -

sin i/sin r = u  --- 1

sin r/ sin e = 1/u  -- 2

Multiplying equation 1 and 2 -

= sin i/ sine = 1

= sin i = sin e

Therefore ∠e = ∠i and are parallel.