Question

A light beam with wavelength 500 nm is reflected constructively from a thin layer of oil having index of refraction 1.25. The oil floats on the top of water of index of refraction 1.33. What is the minimum thickness of the layer of oil

Answer 1

Answer:

t = 200 nm

Explanation:

It is given that,

Wavelength of a light beam is 500 nm

It is reflected constructively from a thin layer of oil having index of refraction 1.25.

The oil floats on the top of water of index of refraction 1.33.

We need to find the minimum thickness of the layer of oil. `

For constructive interference,

$\dfrac{2nt}{\lambda}=m$

m is 1 for minimum thickness

n is refractive index of oil

t is thickness of layer of oil.

So,

$t=\dfrac{m\lambda}{2n}\\\\t=\dfrac{1\times 500\times 10^{-9}}{2\times 1.25}\\\\t=2\times 10^{-7}\ m\\\\t=200\ nm$

So, the minimum thickness of the layer of oil is 200 nm.