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Physics Question on Ray optics and optical instruments

A ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and the latter is equal to 34\frac{3}{4} the angle of prism. The angle of deviation is

A

25∘25^{\circ}

B

30∘30^{\circ}

C

45∘45^{\circ}

D

35∘35^{\circ}

Answer

30∘30^{\circ}

Explanation

Solution

It is observed if ∠i=∠e\angle i=\angle e deviation produced is minimum.
and i=A+δm2 i=\frac{A+\delta_{m}}{2}
Here A=60∘A=60^{\circ}
and ∠i=∠e=34∠A\angle i=\angle e=\frac{3}{4} \angle A
∴δm=2×34×60∘−60∘=30∘\therefore \delta_{m}=2 \times \frac{3}{4} \times 60^{\circ}-60^{\circ}=30^{\circ}