Chapter 19.1, Problem 14SSC

To determine

The distance between the slits.

Answer to Problem 14SSC

  $1.62\times {10}^{-5}\text{m}$

Explanation of Solution

Given:

The wavelength of the light used, $\lambda =542\text{}\text{nm}$

From the figure given,

The distance of the first bright fringe from the central band, $x=4.00\text{cm}$

The distance of the screen from the slit, $L=1.20\text{m}$

Formula used:

For first order bright band, wavelength can be obtained by using:

  $\lambda =\frac{xd}{L}$

Where,

x is the distance of first bright band from the central line on the screen.

d is the distance between slits

L is the distance of screen from the slits.

Calculation:

Using the above-mentioned formula and the given values, the distance between the slits will be,

  $\begin{array}{c}\lambda =\frac{xd}{L}\\ 542\times {10}^{-9}=\frac{\left(4.0\times {10}^{-2}\right)d}{1.2}\\ d=1.62\times {10}^{-5}\text{m}\end{array}$

Conclusion:

Hence, the distance between slits is $1.62\times {10}^{-5}\text{m}$ .