GATE 2023 EC – Question 60
A transparent dielectric coating is applied to glass ($\epsilon_r=4,\ \mu_r=1$) to eliminate the reflection of red light ($\lambda_0=0.75\ \mu$m). The minimum thickness of the dielectric coating, in μm, that can be used is ________ (rounded off to two decimal places).
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Correct answer: 0.12 to 0.14
Explanation
For a quarter-wave anti-reflection coating the coating index must be the geometric mean of the two media: $n_c=\sqrt{n_{air}n_{glass}}=\sqrt{1\times2}=\sqrt2$ (glass $n=\sqrt{\epsilon_r}=2$). The minimum thickness is $d=\dfrac{\lambda_0}{4n_c}=\dfrac{0.75}{4\sqrt2}=0.1326\ \mu$m $\approx0.13\ \mu$m.