First slide

Prism

Question

The angle at which a ray of light be incident on the face of a glass prism of refracting angle $60^{0}$ such that it suffers total internal reflection at the other face is $(μ$ of glass = $\sqrt{2}$ )

Moderate

A

$\sin^{- 1} (\frac{1}{\sqrt{2}} \sin 15^{0})$
B

$\sin^{- 1} (\sqrt{3} \sin 15^{0})$
C

$\sin^{- 1} (\sqrt{2} \sin 15^{0})$
D

$\sin^{- 1} (\sin 15^{0})$

Solution

$μ_{2} \sin r_{2} = μ_{1} \sin i_{2} \sqrt{2} \sin r_{2} = 1 \sin 90 r_{2} = \sin^{- 1} (\frac{1}{\sqrt{2}}) = 45 A = r_{1} + r_{2} 60 = r_{1} + 45 r_{1} = 15 μ_{1} \sin i_{1} = μ_{2} \sin r_{1} (1) \sin i_{1} = \sqrt{2} \sin 15 i_{1} = \sin^{- 1} (\sqrt{2} \sin 15)$

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