Answer to Question #146737 in Optics for Promise Omiponle

Question

A soap bubble is 125 nm thick and illuminated by white light incident perpendicular to its surface.

What is the longest wavelength in nm which is constructively reflected, assuming soap has the same index of refraction as water (n = 1.33)?

Answer 1

Given,

Thickness of the soap bubble $(t)=125nm = 125\times 10^{-9}m$

Refractive index of water $(\mu)=1.33$

We know that the longest wavelength for the constructive wavelength

$\Rightarrow2\mu t = (n-\frac{1}{2})\lambda$

Now, substituting the values,

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

$\Rightarrow \lambda = \frac{2\times 1.33 \times 125\times 10^{-9}m}{\frac{1}{2}}$

$\Rightarrow \lambda = 4\times 1.33\times 125\times 10^{-9}m$

$\Rightarrow \lambda = 0.665\mu m$