Chapter 3, Problem 3.1CYU

Check Your Understanding In the system used in the preceding examples, at what angles are the first and the second bright fringes formed?

To determine

The angles at which the first and second bright fringes are formed.

Answer to Problem 3.1CYU

The angle at which first bright fringe formed is ${3.63}^{\circ }$

The angle at which second bright fringe is formed is ${7.27}^{\circ }$

Explanation of Solution

Given data:

The wavelength of the laser is, $\lambda =633nm$

The separation between the slits is, $d=0.01mm$

Formula used:

  $\sin \theta =\frac{m\lambda }{d}$

Calculation:

Condition for constructive interference is, $\sin \theta =\frac{m\lambda }{d}$

For first bright fringe, $m=1$, therefore the angle of the first fringe can be calculated as

  $\begin{array}{l}\sin \theta =\frac{(1)(633nm)}{0.01mm}=\frac{(1)(633\times {10}^{-9})}{0.01\times {10}^{-3}}=0.063\\ \theta ={\sin }^{-1}0.063={3.63}^{\circ }\end{array}$

For second bright fringe, $m=2$, therefore the angle of the first fringe can be calculated as

  $\begin{array}{l}\sin \theta =\frac{(2)(633nm)}{0.01mm}=\frac{(2)(633\times {10}^{-9})}{0.01\times {10}^{-3}}=0.1266\\ \theta ={\sin }^{-1}0.1266={7.27}^{\circ }\end{array}$

Conclusion:

The wavelength of the laser is, $\lambda =633nm$

The separation between the slits is, $d=0.01mm$