Question

A very thin oil film $\left(n=1.25\right)$floats on water$\left(n=1.33\right)$.

What is the thinnest film that produces a strong reflection for

green light with a wavelength of 500 nm?

Short answer

The oil film has a thickness of$200nm.$

Step-by-step solution

Given data

The thin oil film has a refractive index of $n=1.25$

The reflected green light has a wavelength of$\lambda =500nm=5\times {10}^{-7}m.$

Thickness of the film determination

The thickness of the thinnest film of oil can be obtained by the equation of constructive interference as, , where

For thinnest film, consider

Thus, thickness of the film should be,

$$\begin{gathered} d=\frac{\lambda }{2n} \\ d=\frac{\left(5\times {10}^{-7}\right)m}{2\times 1.25} \\ d=2\times {10}^{-7}m \\ d=200nm \end{gathered}$$