Chapter 20, Problem 72A

To determine

The angle at which light has first-order bright band.

Answer to Problem 72A

  $37.3°$

Explanation of Solution

Given:

The wavelength of the light, $\lambda =527\text{nm}$

Number of lines per centimeter, $n=11,500\text{slits/cm}$

Formula used:

  $n\text{ = }\frac{1}{d\left(\text{cm}\right)}$

Where,

n is the number of lines in diffraction grating per centimeter and d is the distance between the slits.

Wavelength of light can be obtained by:

  $\lambda =d\sin \theta$

Where,

  $\theta$ is the angle at which the first order bright line occurs

d is the distance between the slits.

Calculation:

Now, the distance between the slits will be,

  $\begin{array}{c}d=\frac{1}{n}\\ =\frac{1}{11500}\\ =8.7\times {10}^{-5}\text{cm}\end{array}$

Then, the angle at which the first-order bright band occurs for the light will be,

  $\begin{array}{c}\theta ={\sin }^{-1}\left(\frac{\lambda }{d}\right)\\ ={\sin }^{-1}\left(\frac{527\times {10}^{-9}\text{m}}{8.7\times {10}^{-7}\text{m}}\right)\\ =37.3°\end{array}$

Conclusion:

Hence, the angle at which the light has first-order bright band is $37.3°$ .