Question

Find the refractive index of the liquid if a ray of light strikes surface AB normally and then comes out from face AC at grazing emergence. `(""_aμ_g = 3/2)`

Answer 1

Given:

Prism is equilateral ⇒ angle A = 60°

Ray is incident normally at face AB ⇒ no deviation

Ray emerges at grazing angle from face AC ⇒ e = 90°

Refractive index of air w.r.t. glass (_aμ_g) = `3/2`

To Find:

Refractive index of the liquid (μ)

Calculation:

At face AC, apply Snell’s law:

μ × sin (60°) = 1 × sin (90°)

`μ xx sqrt3/2 = 1`

μ = `2/sqrt3`

Now convert to absolute refractive index:

`μ_"absolute" = ""_aμ_g xx μ`

= `3/2 xx 2/sqrt3`

= `(3 sqrt3)/4`