Question

Anti-reflective coatings on lenses use thin-film interference to eliminate the reflection of a particular color. Suppose a glass lens (ng = 1.55) is covered with a thin film (nf = 1.35) to prevent green light (λ = 521 nm) from being reflected.
a. Write an expression for the minimum thickness the film can have, t.
b. Calculate the minimum thickness, t, in nanometers?

Answer 1

Answer with Explanation:

We are given that

$n_g=1.55$

$n_f=1.35$

$\lambda=521 nm=521\times 10^{-9} m$

$1 nm=10^{-9} m$

a.We have to find the expression for  the minimum thickness the film can have ,t.

Condition for destructive interference

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

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

For minimum thickness m=0

Then, $t=\frac{\lambda}{4n}$

b.Substitute the values

$t=\frac{521\times 10^{-9}}{4\times 1.35}=96.5nm$