A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]

We need the minimum thickness of a transparent film for maximum transmission of green light (550 nm).

In this setup, a film ($$n_f = 2.0$$) is placed on glass ($$n_g = 1.45$$). For maximum transmission, we require minimum reflection, that is, destructive interference of the reflected rays.

Determining the phase changes, light goes from air ($$n = 1$$) to film ($$n = 2.0$$): reflection at the top surface produces a phase change of $$\pi$$ (low to high). Light then goes from film ($$n = 2.0$$) to glass ($$n = 1.45$$): reflection at the bottom surface involves no phase change (high to low), giving a net phase difference of $$\pi$$ between the two reflected rays.

With one phase reversal, destructive interference occurs when:

$$2n_f t = m\lambda$$ ($$m = 1, 2, 3, \ldots$$)

For the minimum nonzero thickness (m = 1),

$$t = \frac{\lambda}{2n_f} = \frac{550}{2 \times 2.0} = \frac{550}{4} = 137.5$$ nm

The minimum thickness is 137.5 nm, which matches Option A. Therefore, the answer is Option A.