Chapter 19.1, Problem 1PP

To determine

The value of the wavelength used.

Answer to Problem 1PP

  $\text{418}\text{nm}$

Explanation of Solution

Given:

The separation of the slits, $d=1.90\times {10}^{-5}\text{m}$

The distance of the first-order yellow band from the central line, $x=13.2\text{mm}$

The distance between the slits and the screen, $L=0.600\text{m}$

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 value of the wavelength used will be,

  $\begin{array}{c}\lambda =\frac{xd}{L}\\ =\frac{\left(13.2\times {10}^{-3}\right)\left(1.90\times {10}^{-5}\right)}{0.600}\\ =418\times {10}^{-9}\text{m}\\ \text{= 418}\text{nm}\end{array}$

Conclusion:

Hence, the value of the wavelength used is $\text{418}\text{nm}$ .