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A thin prism of angle 15° made of glass of refractive index μ₁ = 1.5 is combined with another prism of glass of refractive index μ₂ = 1.75. The combination of the prism produces dispersion without deviation. The angle of the second prism should be

1. 7°
2. 10°
3. 12°
4. 5°

Correct answer: 7°

Solution

For dispersion without deviation, the net deviation caused by the two prisms must cancel out. Using the formula for deviation, δ = (μ - 1)A, and setting the net deviation to zero, we get (1.5 - 1)(15°) = (1.75 - 1)A₂. Solving for A₂ gives A₂ = 7°.

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