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 $640nm$?

• A. $160nm$
• B. $240nm$
• C. $360nm$
• D. $480nm$

Answer 1

The correct option is C $360nm$

Both waves $R_a$ and $R_b$ are out of phase (${180}^o$) with the incident wave, so $R_a$ and $R_b$ are in phase with each other.

thus using $2t=(m+\frac{1}{2})\frac{\lambda }{n}$ for destructive interference (i-e. zero reflection)

let t be the required thickness of the film.

Given ; $n=1.33\lambda =640nm$

for minimum thickness, put $m=0$

this gives $t=120nm$, (but this is not in the options)

for next smallest thickness, put $m=1$ gives $t=360nm$