Chapter 24, Problem 39P

To determine

The wavelengths that is most strongly reflected at the centre of the outer surface.

Answer to Problem 39P

  $643nm$

Explanation of Solution

Given info:

The thickness of soap bubble, $t=120nm$

The refractive index, $n=1.34$

Formula used:

  $\frac{4nt}{2m+1}=\lambda$

Where,

  $m$ is an integer.

  $\lambda$ is wavelength.

  $2t$ is the path difference of two reflected rays. Here, $t$ is the thickness of the soap film.

  $n$ is the refractive index.

Calculation:

Substitute all the given values in formula $\frac{4nt}{2m+1}=\lambda$ :

  $\lambda =\frac{4\left(1.34\right)\left(120nm\right)}{2m+1}=\frac{643nm}{2m+1}$

Therefore, only time the light is visible is when $m=0$

  $\lambda =\frac{643nm}{2\left(0\right)+1}=\frac{643nm}{0+1}=643nm$

Conclusion: The required wavelength is $643nm$ .