A ray of light strikes a plane mirror at an angle of incidence $4 5^{\circ}$ as shown in the figure. After reflection, the ray passes through a prism of refractive index $1.5$ , whose apex angle is $4^{\circ}$ . The angle through which the mirror should be rotated if the total deviation of the ray is to be $9 0^{\circ}$ is

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Prism deviation ρ = A ( μ − 1 ) = 4 × 2 1 ​ = 2 ∘ Total deviation = 9 0 ∘ (reflection) + 2 ∘ (prism) = 9 2 ∘ Net deviation must be 9 0 ∘ , so reflection must give 8 8 ∘ 8 8 ∘ = 18 0 ∘ − 2 i , so i = 4 6 ∘ Mirror must be rotated by 1 ∘ anticlockwise

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