Question

A lens with an index of refraction of 1.60 is to be coated with a material (n = 1.44) that will make the lens nonreflecting for yellow-orange light (? = 515 nm) normally incident on the lens.

What is the minimum required thickness of the coating?

Answer in cm.

Answer 1

For Destructive interferance

$2nd=\left ( m+\frac{1}{2} \right )\lambda$

Where d=Coating Thickness

n=Index of refraction

Minimum Thickness occurs at m=0

$2nd=\frac{1}{2}\lambda$

$=>d=\frac{\lambda }{4n}=\frac{515\times 10^{-9}}{4\times 1.44}=8.94\times 10^{-8} m- or -89.41 nm -or- 8.94\times 10^{-6}cm$