1. Assertion A: The phase difference of two light waves changes if they travel through different media having same thickness, but different refractive indices.

   The phase change acquired by light while travelling a distance $t$ in a medium of refractive index $\mu$ is related to the optical path length: $\text{Optical path length} = \mu t$

   The corresponding phase is $\phi = \frac{2\pi}{\lambda_0}(\mu t)$ where $\lambda_0$ is the wavelength in vacuum.

   So, for two different media of same thickness $t$ but refractive indices $\mu_1$ and $\mu_2$, $\Delta \phi = \frac{2\pi}{\lambda_0}(\mu_1 t - \mu_2 t)=\frac{2\pi t}{\lambda_0}(\mu_1-\mu_2)$

   Since $\mu_1 \neq \mu_2$, phase difference changes.

   Hence, Assertion A is correct.

2. Reason R: The wavelengths of waves are different in different media.

   In a medium of refractive index $\mu$, $\lambda = \frac{\lambda_0}{\mu}$

   Thus, if refractive indices are different, wavelengths in the two media are different.

   Hence, Reason R is correct.

3. Does R correctly explain A?

   Yes. Phase accumulated over thickness $t$ is $\phi = \frac{2\pi t}{\lambda}$ Since wavelength $\lambda$ changes from one medium to another, the phase change over the same thickness also changes.

   Therefore, R is the correct explanation of A.

4. Option check

   • A: Incorrect
   • B: Incorrect
   • C: Incorrect
   • D: Correct

Therefore, the correct answer is D.