Thin Film Interference MCQ - Practice Questions with Answers

Interference effects are commonly observed in thin films when their thickness is comparable to the wavelength of incident light ( if it is too thin as compared to the wavelength of light it appears dark and if it is too thick, this will result in uniform illumination of the film). A thin layer of oil on the water surface and soap bubbles shows various colors in white light due to the interference of waves reflected from the two surfaces of the film.

In thin films, interference takes place between the waves reflected from its two surfaces and waves refracted through it

• Interference in reflected light :

Net path difference between two consecutive waves in the reflected system $=$

$$
\Delta x=2 \mu t \cos r-\frac{\lambda}{2}
$$

(As the ray suffers reflection at the surface of a denser medium an additional phase difference of $\pi$ or a path difference of $\frac{\lambda}{2}$ is introduced.)
1. Condition of constructive interference (maximum intensity):

$$
\begin{aligned}
& \Delta x=n \lambda \\
& \Rightarrow 2 \mu t \cos r+\frac{\lambda}{2}=n \lambda \\
& \Rightarrow 2 \mu t \cos r=\left(n-\frac{1}{2}\right) \lambda \\
& \text { For normal incidence, i.e r=0, so } 2 \mu t=(2 n-1) \frac{\lambda}{2}
\end{aligned}
$$

4. Condition of destructive interference (minimum intensity):

$$
\Delta x=2 \mu t \cos r=(2 n) \frac{\lambda}{2}
$$

And For normal incidence $2 \mu t=n \lambda$

• Interference in refracted light :

Net path difference between two consecutive waves in the refracted system = $\Delta x=2 \mu t \operatorname{cosr}$
1. Condition of constructive interference (maximum intensity):

$$
\Delta x=2 \mu t \cos r=(2 n) \frac{\lambda}{2}
$$

$$
\text { and For normal incidence } 2 \mu t=n \lambda
$$

2. Condition of destructive interference (minimum intensity):

$$
\Delta x=2 \mu t \cos r=(2 n-1) \frac{\lambda}{2}
$$

For normal incidence : $2 \mu t=(2 n-1) \frac{\lambda}{2}$