Question

A transparent dielectric coating is applied to glass $(\varepsilon_r=4,\ \mu_r=1)$ to eliminate the reflection of red light $(\lambda_0=0.75~\mu\text{m})$. The minimum thickness of the dielectric coating, in $\mu$m, that can be used is __________ (rounded off to two decimal places).}

Hint:

N/A

Answer 1

Perfect single-layer AR at normal incidence (air–film–glass), choose film index \(n_f=\sqrt{n_0 n_g}=\sqrt{1. 2}=\sqrt{2}.\)

Step 2: Quarter-wave condition.
Minimum physical thickness for destructive interference:
\[ t_{\min}=\frac{\lambda_f}{4}=\frac{\lambda_0}{4n_f} =\frac{0.75}{4\sqrt{2}}~\mu\text{m} =\frac{0.75}{5.6569}~\mu\text{m}\approx 0.1327~\mu\text{m}. \]

Rounded to two decimals: \(t_{\min}\approx \boxed{0.13~\mu\text{m}}\).