A narrow beam of monochromatic light, PQ, is incident normally on one face of an equiangular glass prism of refractive index 1.45. When the prism is immersed in a certain liquid, the ray makes a grazing emergence along the other face (See figure). Find the refractive index of this liquid.
When the prism is immersed in the liquid and the incident ray emerges along AC, it is clear that it must be incident at the critical angle C on the face AC.
∠A + ∠ARQ = ∠C + ∠ARQ
From the figure, ∴ ∠C = ∠A = 60°
The critical angle when the prism is immersed in the liquid is 60°.
If μg is the refractive index of the material of the prism w.r.t. liquid
Then `""^l µ_g = 1/sin"C" = 1/sin60° = 1/(sqrt3/2) = 2/sqrt3`
`""^l µ_g = 2/sqrt3`
Also, we know that `""^l µ_g =( ""^aµ_g)/( ""^aµ_l)`
`""^aµ_l =( ""^aµ_g)/( ""^l µ_g )`
= `1.45/2 xx sqrt3`
= 1.45 x 0.866