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 $550\ \text{nm}$? [Assume that the light is incident nearly perpendicular to the glass surface.]
Answer: (A) $137.5\ \text{nm}$
Maximum transmission means the two reflected rays interfere destructively.
- Reflection at air $\to$ film ($1 \to 2.0$): phase change of $\pi$.
- Reflection at film $\to$ glass ($2.0 \to 1.45$): no phase change.
So the reflected rays already differ by $\pi$, and they cancel when the path difference is a whole number of wavelengths:
$$2\mu t = m\lambda$$
Minimum non-zero thickness ($m = 1$):
$$t = \frac{\lambda}{2\mu} = \frac{550}{2\times2.0} = 137.5\ \text{nm}$$
Solution by Sreeraj P, M.Sc Physics