Question

Use the above given ray diagram to calculate the angle of incidence. Given that the refractive index of Medium 2 with respect to the Medium 1 is `sqrt 3`.

Answer 1

Given: Refractive index of medium 2 with respect to medium 1 (n₂₁) = `sqrt 3`

In the diagram, the angle between the refracted ray and the horizontal interface in Medium 2 is given as 60°. Since the normal (dashed line) is perpendicular (90°) to the interface:

r = 90° − 60°

= 30°

According to Snell’s Law:

n₂₁ = `(sin i)/(sin r)` 

⇒ `sqrt 3 = (sin i)/(sin 30^circ)`

⇒ sin i = `sqrt 3 xx sin 30^circ`

= `sqrt 3 xx 1/2`

sin i = `sqrt 3/2`    ...(sin 60° = `sqrt 3/2`)

i = 60°

∴ The angle of incidence (i) is 60°.