Question

With the help of above given ray diagram, calculate. the angle of refraction. Given that the refractive index of Medium 2 with respect to Medium 1 is `sqrt 3`.

Answer 1

Given: η₂₁ = `sqrt 3`

The diagram shows that the angle between the ray and the interface is 30°. Since the normal is perpendicular (90°) to the interface:

i = 90° − 30°

= 60°

By using Snell’s law:

η₂₁ = `(sin i)/(sin r)`

`sqrt 3 = (sin 60^circ)/(sin r)`

⇒ sin r = `(sin 60^circ)/sqrt 3`    ...(sin 60° = `sqrt 3/2`)

= `(sqrt 3/2)/sqrt 3`

= `sqrt 3/(2 sqrt 3)`

sin r = `1/2`

r = 30°

∴ The angle of refraction is 30°.