Question

Two light rays having the same wavelength in vacuum are in phase initially. Then, the first ray travels a path \( L_1 \) through a medium of refractive index \( \mu_1 \), while the second ray travels a path \( L_2 \) through a medium of refractive index \( \mu_2 \). The two waves are then combined to observe interference. The phase difference between the two waves is

• A. \( \frac{2\pi}{\lambda} (\mu_1 L_1 - \mu_2 L_2) \)
• B. \( \frac{2\pi}{\lambda} (L_1 - L_2) \)
• C. \( \frac{2\pi}{\lambda} (\mu_1 L_1 - \mu_2 L_2) \)
• D. \( \frac{2\pi}{\lambda} (\mu_1 L_1 + \mu_2 L_2) \)

Hint:

For interference, the phase difference is proportional to the path length and refractive index of the medium.

Answer 1

The Correct Option is A

The phase difference due to different paths in different media is given by \( \Delta \phi = \frac{2\pi}{\lambda} (\mu_1 L_1 - \mu_2 L_2) \).