A thin prism of angle 6° and refractive index for yellow light (n_Y) 1.5 is combined with another prism of angle 5° and n_Y=1.55. The combination produces no dispersion. The net average deviation (δ) produced by the combination is (1/x)°. The value of x is ____________.

Solution

Physics sir · 3 steps

The two prisms point opposite ways, so subtract their deviations, then read x from 1/x.

1. Thin prism deviation. For a thin prism of angle A, the deviation of the mean (yellow) ray is δ = (n_Y - 1)A. In the figure, P₂ is inverted relative to P₁, so its deviation acts in the opposite direction.

   δₙₑₜ = (n₁ - 1)A₁ - (n₂ - 1)A₂

2. Put in numbers. P₁ gives (1.5 - 1) × 6° = 3°. P₂ gives (1.55 - 1) × 5° = 2.75°. So δₙₑₜ = 3° - 2.75° = 0.25° = (1/4)°.
3. So. Matching (1/x)° with (1/4)° gives x = 4.

The common slip: 0.25. Writing the deviation itself as the answer gives 0.25, but the question asks for x in (1/x)°, which is 4.

The idea to keep. In an achromatic pair the prisms are inverted, so dispersions cancel but deviations only partly cancel. Net mean deviation is the difference of the two (n_Y - 1)A values.

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