Chapter 22, Problem 113A

To determine

The distance between the slits.

Answer to Problem 113A

  $1.45\times {10}^{-4}\text{m}$

Explanation of Solution

Given:

The wavelength of the laser light, $\lambda =478\text{nm}$

The distance of the screen from the slits, $L=0.91\text{m}$

The distance of the first-order bright band from the central line, $x=3.00\text{mm}$

Formula used:

Wavelength from double-slit experiment is given by,

  $\lambda =\frac{xd}{L}$

Where,

x is the distance of first bright band from the central line on the screen, d is the distance between the slits and L is the distance of the screen from the slits.

Calculation:

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

  $\begin{array}{l}\lambda =\frac{xd}{L}\\ 478\times {10}^{-9}=\frac{\left(3.00\times {10}^{-3}\right)d}{0.91}\\ d=1.45\times {10}^{-4}\text{m}\end{array}$

Conclusion:

Hence, the distance between the slits is $1.45\times {10}^{-4}\text{m}$ .