Chapter 24, Problem 27P

To determine

The angle for the second order.

Answer to Problem 27P

  $4.43°$

Explanation of Solution

Given info:

Wavelength of light, $\lambda =560nm=560\times {10}^{-9}m$

Spacing between gratings, $d=1.45\times {10}^{-3}cm=1.45\times {10}^{-5}m$

Order, $m=2$

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 angle for the second order:

  $\left(1.45\times {10}^{-5}\right)\sin \theta =\left(2\right)\left(560\times {10}^{-9}m\right)$

This gives, $\sin \theta =\frac{\left(2\right)\left(560\times {10}^{-9}m\right)}{\left(1.45\times {10}^{-5}\right)}=0.0772$

  $\theta =0.0772=4.43°$

Conclusion:

The angle is $4.43°$ .