Chapter 19.1, Problem 4PP

To determine

The distance between the screen and the slits.

Answer to Problem 4PP

  $0.755\text{m}$

Explanation of Solution

Given:

The wavelength of the yellow-orange light, $\lambda =596\text{}\text{nm}$

The separation of the slits, $d=2.25\times {10}^{-5}\text{m}$

The distance of the first-order yellow band from the central line, $x=2.00\times {10}^{-2}\text{m}$

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 of the screen from the slits will be,

  $\begin{array}{c}\lambda =\frac{xd}{L}\\ 596\times {10}^{-9}=\frac{\left(2.00\times {10}^{-2}\right)\left(2.25\times {10}^{-5}\right)}{L}\\ L=0.755\text{m}\end{array}$

Conclusion:

Hence, the distance of the screen from the slits is $0.755\text{m}$ .