Chapter 24, Problem 2P

To determine

The distance between slits.

Answer to Problem 2P

  $5.9\times {10}^{-6}m$

Explanation of Solution

Given info:

Angle, $\theta =18°$

Wavelength, $\lambda =610nm=610\times {10}^{-9}m$

Order, $m=3$

Formula used:

  $\sin \theta =\frac{m\lambda }{d}$

Where,

  $m$ is an integer

  $\lambda$ is wavelength

  $d$ is a distance

Calculation:

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

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

Substitute the given values in formula, $d\sin \theta =m\lambda$

  $d\sin \left(18°\right)=3\left(610\times {10}^{-9}m\right)$

  $d=5.9\times {10}^{-6}m$

Conclusion: The required value is $5.9\times {10}^{-6}m$ .