A prism of angle A = 1ᵒ has a refractive index μ = 1.5. A good estimate for the minimum angle of deviation (in degrees) is close to N/10.
Value of N is ____.

Solution

Physics sir · 3 steps

A 1° prism is a thin prism, so the deviation is just (μ - 1)A. No sine formula needed.

1. Thin prism. For a small angle, sin θ ≈ θ in radians. With this, the full prism formula μ = sin((A+δₘ)/2)/(sin A/2) becomes μ = (A + δₘ)/A.

   δₘ = (μ - 1)A

2. Put in numbers. δₘ = (1.5 - 1) × 1° = 0.5°. Both sides of the formula are angles, so you can keep degrees and do not need radians.
3. So. N/10 = 0.5, so N = 5.

The common slip: 0.5. Reporting the deviation itself gives 0.5. The question asks for N, which is 10 δₘ = 5.

The idea to keep. For a thin prism, the deviation is (μ - 1)A and does not depend on the angle of incidence. Use it whenever A is only a few degrees.

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