Chapter 19.2, Problem 19PP

To determine

The wavelength of the light.

Answer to Problem 19PP

  $590\times {10}^{-8}\text{m}$

Explanation of Solution

Given:

The width of the central bright band, $2x_1=24.0\text{mm}$

The width of the slits, $w=0.0295\text{mm}$

The distance of the screen from the slit, $L=60.0\text{cm}$

Formula used:

The width of bright band in Single-Slit Diffraction is given by,

  $2x_1=\frac{2\lambda L}{w}$

Where,

L = distance between screen and slit

  $\begin{array}{l}\lambda =\text{wavelength}\\ w=\text{ width of the slits}\end{array}$

Calculation:

Using the above mentioned formula and the given values, the wavelength of the light used will be,

  $\begin{array}{c}2x_1=\frac{2\lambda L}{w}\\ 24\times {10}^{-3}=\frac{2\lambda \left(0.60\right)}{\left(0.0295\times {10}^{-3}\right)}\\ \lambda =590\times {10}^{-8}\text{m}\end{array}$

Conclusion:

Hence, the wavelength of the light used is $590\times {10}^{-8}\text{m}$ .