Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction.
Reason R: The wavelengths of waves are different in different media.
In the light of the above statements, choose the most appropriate answer from the options given below

Solution

Physics sir · 4 steps

Same thickness, different wavelengths inside: count how many waves fit, and the phase gap appears.

1. Check Reason R. When light enters a medium its frequency stays the same, but its speed drops to c/μ. So the wavelength becomes λ/μ, which is different in media with different μ. R is correct.
2. Phase gained inside. A wave crossing a thickness t picks up a phase of 2π for every wavelength that fits in t. With wavelength λ/μ, that phase is (2π μ t)/λ.

   Δφ = (2π t)/(λ/μ₁) - (2π t)/(λ/μ₂) = (2π t)/λ(μ₁ - μ₂)

3. Check Assertion A. If μ₁ ≠ μ₂, then Δφ ≠ 0, so the phase difference between the two waves changes. A is correct, and it changes because the wavelengths in the two media differ.
4. So. Both statements are correct and R is exactly the reason for A, which is option (d).

The idea to keep. Inside a medium the wavelength shrinks to λ/μ, so a slab of thickness t adds a phase of 2π/λμ t. Different μ means different phase, which is why optical path is μ t, not t.

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