Consider a light ray travelling in air is incident into a medium of refractive index √2n. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

Solution

Physics sir · 4 steps

Put i = 2r into Snell's law and use sin 2r = 2 sin r cos r. The sin r cancels and cos r drops out.

1. Snell's law. Light goes from air (μ = 1) into the medium, so sin i = √2n sin r. The question also tells you i = 2r.

   sin 2r = 2 sin r cos r = √2n sin r

2. Cancel sin r. Since sin r ≠ 0, divide both sides by it: 2 cos r = √2n. This gives cos r = √2n/2 = √(n/2).
3. Angle of refraction. So r = cos⁻¹(√(n/2)). The question asks for the angle of incidence, which is twice this.
4. So. i = 2r = 2 cos⁻¹(√(n/2)), which is option (d).

The idea to keep. When one angle is twice the other, write the bigger sine with the double-angle formula. The common sin r cancels and you are left with a clean cosine.

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