A ray of light is incident on first face of an equilateral glass prism at an angle of incidence ' i '. The emergent ray just grazes along the adjacent face. The refractive index of the the p

Question

A ray of light is incident on first face of an equilateral glass prism at an angle of incidence ' i '. The emergent ray just grazes along the adjacent face. The refractive index of the the prism is 2 ​ . The value of angle of incidence at first face is ( sin 4 5 ∘ = 2 ​ 1 ​ , sin 9 0 ∘ = 1 )

TestHub · Accepted Answer

For an equilateral prism, the angle of the prism is $A = 6 0^{\circ}$ .

At the second face, the emergent ray just grazes the surface, so the angle of emergence is $e = 9 0^{\circ}$ .

Using Snell's law at the second face:

$μ sin r_{2} = sin e$

$2 sin r_{2} = sin 9 0^{\circ} = 1$

$sin r_{2} = \frac{1}{2}$

$r_{2} = 4 5^{\circ}$

Using the relation for the angle of the prism:

$r_{1} + r_{2} = A$

$r_{1} + 4 5^{\circ} = 6 0^{\circ}$

$r_{1} = 1 5^{\circ}$

Using Snell's law at the first face:

$sin i = μ sin r_{1}$

$sin i = 2 sin 1 5^{\circ}$

$i = sin^{- 1} (2 sin 1 5^{\circ})$

Answer: $sin^{- 1} (2 sin 1 5^{\circ})$

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