Question

(i) A ray of light incident on face AB of an equilateral glass prism, shows minimum deviation of 30°. Calculate the speed of light through the prism.

(ii) Find the angle of incidence at face AB so that the emergent ray grazes along the face AC.

Answer 1

(i) μ = `sin((A  +  δ_m)/2)/(sin(A/2))`

= `(sin((60  +  30)/2))/(sin(60^circ/2))`

= `sqrt(2)`

Also μ = `c/v`

⇒ v = `(3 xx 10^8)/sqrt(2)` m/s

(ii)

At face AC, let the angle of incidence be r₂. For grazing ray, e = 90°

⇒ μ = `1/sinr_2`

⇒ r₂ = `sin^-1(1/sqrt(2))` = 45°

Let the angle of refraction at face AB be r₁.

Now r₁ + r₂ = A

∴ r₁ = A – r₂ = 60º – 45º = 15º

Let the angle of incidence at this face be i

μ = `sini/sin r_1`

⇒ `sqrt(2) =  sini/sin15^circ`

∴ i = `sin^-1 (sqrt(2).sin15^circ)` = 21.5º