Question

A parallel beam of light of wavelength 560 nm falls on a thin film of oil (refractive index = 1.4). What should be the minimum thickness of the film so that it strongly reflects the light?

Answer 1

Given:
Wavelength of light used, $\mathrm{\lambda }=560\times {10}^{-9}\mathrm{m}$
Refractive index of the oil film, $\mathrm{\mu }=1.4$
Let the thickness of the film for strong reflection be t.
The condition for strong reflection is
$$\begin{gathered} 2\mathrm{\mu }t=\left(2n+1\right)\frac{\lambda }{2} \\ \Rightarrow t=\left(2n+1\right)\frac{\lambda }{4\mathrm{\mu }} \end{gathered}$$
where n is an integer.
For minimum thickness, putting n = 0, we get:
$$\begin{gathered} t=\frac{\lambda }{4\mathrm{\mu }} \\ =\frac{560\times {10}^{-9}}{4\times 1.4} \\ ={10}^{-7}\mathrm{m}=100\mathrm{nm} \end{gathered}$$
Therefore, the minimum thickness of the oil film so that it strongly reflects the light is 100 nm.