Two light waves having the same wavelength λ in vacuum are in phase initially. Then the first wave travels a path L₁ through a medium of refractive index n₁ while the second wave travels a path of length L₂ through a medium of refractive index n₂ . After this the phase difference between the two waves is :

Solution

Physics sir · 3 steps

In a medium the wavelength shrinks to λ/n, so turn each path into optical path nL.

1. Wavelength shrinks. In a medium of refractive index n the frequency stays the same, but the speed drops to c/n. So the wavelength becomes λ/n.
2. Phase along a path. Each wavelength travelled adds 2π of phase. Over length L the wave fits L/(λ/n) = nL/λ wavelengths, so it gains a phase of 2π/λ nL.

   Δφ = 2π/λn₁ L₁ - 2π/λn₂ L₂ = 2π/λ(n₁ L₁ - n₂ L₂)

3. So. The waves started in phase, so the difference in optical paths gives the whole phase difference. That is option (a).

The idea to keep. Phase difference is 2π/λ times the optical path difference, and the optical path through a medium is nL. Always pair each n with its own L.

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