A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ____________° (in degree). (Round off to the Nearest Integer)

Solution

Physics sir · 4 steps

Achromatism fixes the ratio of the two deviations. Then the net 2° tells you each one.

1. No dispersion. Achromatic means the angular dispersions of the two prisms cancel. Angular dispersion is ωδ, so ω_cδ_c = ω_fδ_f, with the two prisms placed opposite each other.

   0.02 δ_c = 0.03 δ_f ⇒ δ_f = 2/3δ_c

2. Net deviation. The prisms deviate light in opposite directions, so the net deviation is δ_c - δ_f = 1/3δ_c = 2°. That gives δ_c = 6° and δ_f = 4°.
3. Thin prism. For a thin prism δ = (μ - 1)A. For crown glass 6° = (1.5 - 1)A_c, so A_c = 6°/0.5 = 12°.
4. So. The refracting angle of the crown glass prism is 12°.

The common slip: 4. Treating the net 2° as the crown prism's own deviation gives A = 2°/0.5 = 4, not 12. The crown deviation is 6°, and the flint prism takes back 4° of it.

The idea to keep. In an achromatic pair, set ω₁δ₁ = ω₂δ₂ and take the net deviation as the difference. Then use δ = (μ-1)A for each prism.

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