Prism

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Question

A ray of light is incident at an angle of $60^{0}$ on one face of a prism which has refracting angle of $30^{0}$ . The ray emerging out of the prism makes an angle of $30^{0}$ with the incident ray. Find the value of refractive index of the material of the prism .

Moderate

Solution

$A + δ = i + e 30 + 30 = 60 + e e = 0 ∴ r_{2} = 0 A = r_{1} + r_{2} 30 = r_{1} + 0 A p p l y S n e l l' s l a w a t f i r s t s u r f a c e . (1) \times \sin i = (μ) \times \sin r_{1} \Rightarrow μ = \frac{\sin 60^{o}}{\sin 30^{o}} = \sqrt{3} = 1.73$

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