Question

A parallel beam of light of wavelength $560\text{nm}$ 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?

• A. $100\text{nm}$
• B. $200\text{nm}$
• C. $300\text{nm}$
• D. $500\text{nm}$

Answer 1

The correct option is A $100\text{nm}$

Given :

Wavelength of light,

$\lambda =560\text{nm}=560\times {10}^{-9}\text{m}$

Refractive index of oil, $\mu =1.4$

For strong reflection,

$2\mu t=(2n+1)\frac{\lambda }{2}$

$\Rightarrow t=\frac{(2n+1)\lambda }{4\mu }$

For minimum thickness, $n=0$.

So,

$t=\frac{\lambda }{4\mu }$

$\Rightarrow t=\frac{560\times {10}^{-9}}{4\times 1.4}={10}^{-7}\text{m}=100\text{nm}$

Hence, option $\left(A\right)$ is the correct answer.