Question

Consider a film of thickness $L$ as shown in four different cases below. Notice the observation of film with perpendicularly falling light. Mark the correct statement(s). (Take $L=1.5\lambda$)

• A. For (1) and (2), the reflection at film interfaces causes zero phase difference for two reflected rays
• B. For 92) and (3), the reflection at film interfaces causes a phase difference of $\pi$ for two reflected rays.
• C. For (1), the film will appear dark, if it is observed through reflected rays from film interfaces
• D. For (3), the film will appear dark, if it is observed through reflected rays from film interfaces

Answer 1

Answer: (B), (D)

For 92) and (3), the reflection at film interfaces causes a phase difference of $\pi$ for two reflected rays.
For (3), the film will appear dark, if it is observed through reflected rays from film interfaces

Reflection light from a surface of higher refractive index causes a change of phase by $\pi$.

For (1),

Path difference between the rays due to extra path traveled by ray 2 =$2L=3\lambda$

Total phase difference between the rays=$3\lambda \left(\frac{2\pi }{\lambda }\right)=6\pi$ or $0$

For 2,

Phase change in ray 2 by reflection from denser medium=$\pi$

Path difference between the rays due to extra path traveled by ray 2 =$2L=3\lambda$

Total phase difference between the rays=$3\lambda \left(\frac{2\pi }{\lambda }\right)+\pi =7\pi$ or $\pi$

For 3,

Phase change in ray 2 by reflection from denser medium=$\pi$

Path difference between the rays due to extra path traveled by ray 2 =$2L=3\lambda$

Total phase difference between the rays=$3\lambda \left(\frac{2\pi }{\lambda }\right)+\pi =7\pi$ or $\pi$

Thus the film appears dark due to destructive interference.