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Questions
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.
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Solution
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/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
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