Three experiments involving a thin film (in air) are shown. If t denotes the film thickness and $\lambda$ denotes the wavelength of the light in the film, which experiments will produce constructive interference as seen by the observer?
A) I only
B) II only
C) III only
D) I and III only
E) II and III only

Question

Three experiments involving a thin film (in air) are shown. If t denotes the film thickness and $\lambda$ denotes the wavelength of the light in the film, which experiments will produce constructive interference as seen by the observer? 
A) I only 
B) II only 
C) III only 
D) I and III only 
E) II and III only

Quizplus · Accepted Answer

For constructive interference to occur, the path difference between the reflected waves must be an integer multiple of the wavelength. This means that $2t = m\lambda/2$ where $m$ is an integer.

In Experiment I, the path difference is $2t$, so to get constructive interference we need $2t = m\lambda/2$. This condition can be satisfied for certain values of $t$ and $\lambda$ only.

In Experiment II, the path difference is $2\sqrt{2}t$, so to get constructive interference we need $2\sqrt{2}t = m\lambda/2$. This condition can be satisfied for certain values of $t$ and $\lambda$ only.

In Experiment III, the path difference is $2t+\lambda/2$, so to get constructive interference we need $2t+\lambda/2 = m\lambda/2$. This condition can be satisfied for certain values of $t$ and $\lambda$ only.

Thus, experiments I and III can produce constructive interference under certain conditions, but experiment II cannot. Therefore, the answer is D.

Three Experiments Involving a Thin Film (In Air) Are Shown λ\lambdaλ

Three Experiments Involving a Thin Film (In Air) Are Shown $\lambda$