Question

A thin film with index of refraction $1.50$ coats a glass lens with index of refraction $1.80$. What is the minimum thickness of the film that will strongly reflect light with wavelength $600nm$?

• A. $150nm$
• B. $200nm$
• C. $300nm$
• D. $450nm$

Answer 1

The correct option is B $200nm$

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 $2t=m\lambda /n$ for constructive interference (i-e. complete reflection)

let t be the minimum thickness of the film( i-e. $m=1$)

Given ; $n=1.5\lambda =600nm$

$2t=\frac{1\times 600nm}{1.5}$

On solving $t=200nm$