Chapter 24, Problem 34P

To determine

The highest spectral orderthat can be seen.

Answer to Problem 34P

Two

Explanation of Solution

Given info:

The maximum Angle, $\theta =90°$

Number of grating per unit length $N=6000lines/cm$

Wavelength, $\lambda =633nm=633\times {10}^{-9}m$

Formula used:

  $\sin \theta =\frac{m\lambda }{d}$

Where,

  $m$ is an integer

  $\lambda$ is wavelength

  $d$ is distance between slits

Calculation:

In constructive interference, path difference is an integer multiple of wavelength.

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

Calculation for $m$ by using $d\sin \theta =m\lambda$

  $\left[\frac{1}{\left(6000lines/m\right)}\right]\left({10}^{-2}m/cm\right)\sin 90°=\left(m\right)\left(633\times {10}^{-9}m\right)$

  $m=2.63$

So, two orders can be seen on each side of the central white line.

Conclusion:

Two orders can be seen on each side of the central white line.