Chapter 24, Problem 43P

To determine

To Compare: The thickness of centre with the edges.

Answer to Problem 43P

  $8500nm$

Explanation of Solution

Given info:

Wavelength, $\lambda =550nm$

Order, $m=31$

Formula used:

Dark bands will occur when $2t=m\lambda ,m=0,1,2,\mathrm{...}$

The light rays are perpendicular to the plates, the extra path length equals $2t$ , where $t$ , thickness of the air gap at any point is.

Where,

  $m$ is an integer.

  $t$ is the thickness of the film.

  $\lambda$ is wavelength.

Calculation:

Let $m$ equal to the number of rings.

The equation can now be written as $t=\frac{1}{2}m\lambda$

  $t=\frac{1}{2}m\lambda =\frac{1}{2}\left(31\right)\left(550\right)=8525nm$

Conclusion:

The required thickness is $8525nm$ .