When you put an anti-reflective thin film on a lens of sunglasses for example, how do they account for all of the wavelengths within the visible spectrum?

In order to counter reflection, you would need destructive interference of the waves reflected back into the eyes of the wearer.

We know that $$L = \frac{\lambda}{4n_2}$$ for destuctive interference where $L$ is the width of the thin lens and $n_2$ is the refraction index of the sunglasses’ lens.

How do they account for the entire range of 700-400nm of wavelengths for visible light? Do they stack a few of these layers on each other? Do they just take the average wavelength in that range?


In the case where we have an anti reflective coating with a thickness $L_{layer}=\frac{\lambda_{medium}}{4}$ and with a layer refractive index of $n=\sqrt{n_0n_1}$ where $n_0$ is the refractive index of the glass and $n_1$ is the refractive index of air the glasses will be reflective for, as you know, a very narrow set of wavelengths.

By instead doing similar coatings but with alternating refractive indexes, the freflectivity can be minimzed over a set of wavelengths. Given enough layers, the visible spectrum will be covered.


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