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A horizontal ray is incident on a right-angled prism whose refracting angle is 4°, as shown in the figure. If the refractive index of the material of the prism is 1.5, the angle of emergence is ______.

Asked in RS Academy GUJCET booklet · Deviation and minimum deviation

Figure: Deviation and minimum deviation
Answer: (2) 6°

Step-by-step solution

Given: a right-angled prism of refracting angle A = 4° and n = 1.5; the incident ray is horizontal and so meets the vertical face square on.

Idea: take the two refracting faces one at a time.

At the first face the ray travels along the normal, so it enters without bending: r₁ = 0.

For any prism r₁+r₂ = A, so inside the glass the ray meets the slanted face at r₂ = 4° to its normal.

Snell's law at that face, going from glass into air: n sin r₂ = sin e, so sin e = 1.5×sin 4° = 1.5×0.0698 = 0.1047.

e = 6°, and as a check the deviation is e-r₂ = 2°, which is just A(n-1) = 4°×0.5 for a thin prism.

Why the other options are wrong

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