JEE Physics 2023 Question with Solution

Given: Assertion $A$ states that the phase difference of two light waves changes if they travel through different media of same thickness but different refractive indices. Reason $R$ states that wavelengths of waves are different in different media.

Find: Whether $A$ and $R$ are correct, and whether $R$ explains $A$.

For light in a medium,

$$v = \frac{c}{\mu}$$

Also,

$$v = f\lambda = \frac{c}{\mu}$$

Therefore,

$$\lambda \propto \frac{1}{\mu}$$

So, when light travels through different media, its wavelength changes because the refractive index changes.

The phase change over a path depends on wavelength. For a given thickness, if the wavelength changes in different media, the phase difference also changes.

Using the relation given in the solution,

$$\Delta Q = \frac{2\pi}{\lambda}$$

Thus, statement $R$ correctly explains why the phase difference changes in different media.

Therefore, both $A$ and $R$ are correct, and $R$ is the correct explanation of $A$. The correct option is A.

Given: Different media have different refractive indices but the same thickness.

Find: Why phase difference changes.

The frequency of light does not change when it enters another medium, but its speed changes according to

$$v = \frac{c}{\mu}$$

Hence the wavelength becomes

$$\lambda = \frac{v}{f}$$

Since $v$ changes with medium while $f$ remains constant, $\lambda$ also changes.

Phase accumulated over travel through a medium depends on how many wavelengths fit into the path length. Therefore, for the same thickness, a different wavelength produces a different phase change.

So the reason directly explains the assertion, and the correct option is A.