Question

 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. 

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 as shown in the figure. Find the refractive index of this liquid.

Answer 1

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 μ_g is the refractive index of the material of the prism w.r.t. liquid

Then `""^l µ_g = 1/sinC`

= `1/sin60°`

= `1/(sqrt3/2)`

= `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 × 0.866 

= 1.256