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A Narrow Beam of Monochromatic Light, Pq, is Incident Normally on One Face of an Equiangular Glass Prism of Refractive Index 1.45. When Th - Physics (Theory)

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 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. 

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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 

= 1.256

Concept: Dispersion by a Prism
  Is there an error in this question or solution?
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