Question

High quality camera lenses are often coated to prevent reflection. A lens has an optical index of refraction of $1.72$ and a coating with an optical index of refraction of $1.31$. For near normal incidence the minimum thickness of the coating to prevent reflection for wavelength of $5.3\times {10}^{-7}m$ is :

• A. $0.75\mu m$
• B. $0.2\mu m$
• C. $0.1\mu m$
• D. $1.75\mu m$

Answer 1

The correct option is C $0.1\mu m$

Using the destructive interference equation so that no light is reflected,
$2t=\frac{{\lambda }_{film}}{2}$
where $t$ is the thickness of coating.
and, ${\lambda }_{film}=\lambda /refractiveindex=5.3\ast {10}^{-7}/1.31=4.04\ast {10}^{-7}$
So thickness, $t=4.04\ast {10}^{-7}/4\approx 0.1\ast {10}^{-6}=0.1\mu m$