A ray is incident normally on a right angle prism whose refractive index is $\sqrt{3}$ and prism angle $α = 30 °$ , after crossing prism ray passes through glass sphere. It strikes the glass sphere of same refractive index, at $\frac{R}{2}$ distance from principal axis, as shown in the figure, sphere is half polished. The net angle of deviation of the incident ray is

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$180^{0}$

$60^{0}$

$45^{0}$

$90^{0}$

answer is A.

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Detailed Solution

Given refractive index $μ = \sqrt{3}$
Angle of prism $α = 30^{\circ}$
According to Snell’s law,
$\begin{array}{l} μ \sin α = 1 \cdot \sin β \\ \sqrt{3} \sin 30^{\circ} = \sin β \\ \Rightarrow β = 60^{\circ} \Rightarrow β - α = 30^{\circ} \end{array}$

$\sin θ = \frac{(\frac{R}{2})}{R} = \frac{1}{2} \Rightarrow θ = 30^{\circ} = β - α$

$∴$ The incident ray on the sphere is directed radially.
$∴$ It will be reflected back and will retrace the path
$∴$ Angle of deviation is $180^{\circ}$

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