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,

\[\lambda = 560 \times {10}^{- 9} m\]

Refractive index of the oil film, \[\mu = 1 . 4\]

Let the thickness of the film for strong reflection be t.

The condition for strong reflection is

\[2\mu t = \left( 2n + 1 \right)\frac{\lambda}{2}\]

\[ \Rightarrow t = \left( 2n + 1 \right)\frac{\lambda}{4\mu}\]

where n is an integer.

For minimum thickness, putting n = 0, we get

\[t = \frac{\lambda}{4\mu}\]

\[ = \frac{560 \times {10}^{- 9}}{4 \times 1 . 4}\]

\[ = {10}^{- 7} m = 100 nm\]

Therefore, the minimum thickness of the oil film so that it strongly reflects the light is 100 nm.