Chapter 24, Problem 30P

To determine

The number of complete spectral orders.

Answer to Problem 30P

One full order

Explanation of Solution

Given info:

Wavelength of the light, $\lambda =700nm=700\times {10}^{-9}m$

Angle, $\theta =90°$ (Because the angle increases with wavelength, to have a complete order, use the largest wavelength).

The maximum angle is $\theta =90°$ .

Number of grating per unit length, $N=8300lines/cm$

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, the path difference is an integer multiple of the wavelength.

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

Substitute the given values:

  $\left[\frac{1}{\left(8300lines/cm\right)}\right]\left({10}^{-2}m/cm\right)\sin 90°=m\left(700\times {10}^{-9}m\right)$

This gives, $m=1.70$

So, only one full order can be seen on each side of central white line.

Conclusion:

The required order: one full order