Show that a ray of light passing through layers of transparent media separated by parallel boundaries, nsin i = a where a is a constant and n is the refractive index of the medium containing angle i.

Show that a ray of light passing through layers of transparent media separated by parallel boundaries,

nsin i = a where a is a constant and n is the refractive index of the medium containing angle i.

Solution

Consider a ray of light moving from air through a series of media 1, 2 and then finally emerge into air as shown.

At air – medium 1 interface, Snell’s law gives  (sin i /sin i₁) = n₁

=> Sin i_a = n₁sin i₁ …………………………….. (i)

At air – medium 2 interface, Snell’s law gives (sin i /sin i₂) = n₂

=> Sin i_a = n₂sin i₂ …………………………….. (ii)

Equating equation (i) and (ii) gives

n₁ sin i₁  =  n₂ sin i₂.

therefore,  n sin i = a constant.