A glass slab of refractive index \({\mu }_{0}=1.44\) is coated with a thin film of refractive index \({\mu }_{f}=2\). Th…

To achieve maximum transmission of green light, the thin film must cause destructive interference for the light reflected from its top and bottom surfaces. This is a standard case of thin-film interference, and the condition for minimum thickness for maximum transmission (destructive reflection) is:

\(2\mathrm{n}\mathrm{t}=\mathrm{m}\lambda\)

where: n is the refractive index of the film, t is the thickness of the film, \(\lambda\) is the wavelength of light in the medium of the film, m is the order of interference (minimum for the thinnest film).

Here, m = 1

So, \(\mathrm{t}=\frac{\mathrm{m}\lambda }{2\mathrm{n}}=\frac{1\times 5000}{2\times 2}=1250\overset{^\circ }{\mathrm{A}}\)