Chapter 24, Problem 28P

To determine

The wavelength of light that is being used.

Answer to Problem 28P

  $447nm$

Explanation of Solution

Given info:

Number of lines per unit length, $N=3500lines/cm$

Spacing between lines, $d=\frac{1}{N}$

Angle at which $3^{rd}$ order fringe is formed, $\theta =28°$

Formula used:

  $\sin \theta =\frac{m\lambda }{d}$

Where,

  $m$ is an integer.

  $\lambda$ is wavelength.

  $d$ is distance between slits.

Calculation:

The path difference is an integer multiple of the wavelength in constructive interference.

Rearrange the given formula: $\sin \theta =\frac{m\lambda }{d}$ . So, $d\sin \theta =m\lambda$

Calculate the wavelength form:

  $\left[\frac{1}{3500lines/cm}\right]\left({10}^{-2}m/cm\right)\sin 28.0°=3\lambda$

This gives, $\lambda =4.47\times {10}^{-7}m=447nm$

Conclusion:

The required wavelength is $447nm$ .