Chapter 24, Problem 69GP

To determine

The distance between the wings that appears.

Answer to Problem 69GP

  $590\text{nm}$

Explanation of Solution

Given data:

Wavelength, $\lambda =460\times {10}^{-9}\text{m}$

The angles of normal, $\text{θ}=51°$

Formula used:

  $d\sin \theta =m\lambda$

Where,

  $d$ is the distance between lines.

  $\lambda$ is wavelength.

  $\theta$ is angle of the normal.

Calculation:

The lines are acting like a grating.

Consider first order and find the separation of the lines from the formula, $d\sin \theta =m\lambda$

  $\therefore d\sin 51°=\left(1\right)\left(460\times {10}^{-9}\text{m}\right)$

  $\therefore d=5.9\times {10}^{-7}\text{m}$

  $\therefore d=590\text{nm}$

Conclusion: The distance between the lines is $590\text{nm}$ .