A thin prism P₁ with an angle 6° and made of glass of refractive index 1.54 is combined with another prism P₂ made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism P₂ is

Solution

Physics sir · 4 steps

No average deviation means the two thin-prism deviations cancel, so set (μ - 1)A equal for both prisms.

1. Thin prism deviation. A thin prism of angle A and refractive index μ deviates a ray by δ = (μ - 1)A. The thicker the bending power (μ - 1), the smaller the angle you need for the same deviation.
2. Zero net deviation. The prisms are placed with their bases opposite, so their deviations subtract. For no average deviation the two must be equal in size.

   (μ₁ - 1)A₁ = (μ₂ - 1)A₂

3. Put in numbers. (1.54 - 1) × 6° = (1.72 - 1)A₂, which gives 0.54 × 6° = 0.72 A₂, so 3.24° = 0.72 A₂.
4. So. A₂ = 3.24°/0.72 = 4.5°, which is option (a).

The idea to keep. For thin prisms in combination, deviation is (μ - 1)A. Equate these for zero deviation, or equate (μᵥ - μᵣ)A for zero dispersion.

Answer from the NTA final answer key. Solution by PrepWiser.