What is antireflection coating? What should be the refractive index and minimum thickness of the coating?

Antireflection (AR) coating: A thin transparent film, for example MgF₂, deposited on a lens or glass surface. Light reflected from its upper and lower surfaces interferes destructively, so reflection is reduced to almost zero and transmission increases. It is used on camera lenses, spectacles and solar cells.

Both reflections are rarer-to-denser (air → film → glass), so each adds a phase change of π and the two cancel. For normal incidence, the path difference is \(2\mu t\).

Thickness condition (destructive interference): \(2\mu t=(2n+1)\dfrac{\lambda}{2}\). The minimum is at n = 0:

\[ \boxed{t_{min}=\frac{\lambda}{4\mu}} \]

So the optical thickness is a quarter wavelength.

Refractive index condition: For complete cancellation the two reflected amplitudes must be equal:

\[ \frac{\mu-1}{\mu+1}=\frac{\mu_g-\mu}{\mu_g+\mu}\Rightarrow\boxed{\mu=\sqrt{\mu_g}} \]

Here \(\mu_g\) is the index of the glass. Example: for glass with \(\mu_g=1.5\), \(\mu\approx1.22\). MgF₂ (μ = 1.38) is the practical choice.