Question

A thin film with index of refraction $1.33$ coats a glass lens with index of refraction $1.50$. Which of the following choices is the smallest film thickness that will not reflect light with wavelength $640\text{nm}$ ?

• A. $120\text{nm}$
• B. $240\text{nm}$
• C. $360\text{nm}$
• D. $480\text{nm}$

Answer 1

The correct option is A $120\text{nm}$

Since, both waves $R_a$ and $R_b$ are reflected from denser medium, so $R_a$ and $R_b$ are in phase with each other.

Thus, for destructive interference (i.e. Zero reflection)

$2\mu t=(m+\frac{1}{2})\lambda$

Where $t$ is the required thickness of the film

And $\mu$ is the refractive index of thin film

For minimum thickness, take $m=0$

$\Rightarrow t=\frac{640}{4\times 1.33}=120\text{nm}$

Hence, $\left(\text{A}\right)$ is the correct answer.