Question

What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of${}^{\mathbf{30}\mathbf{.}\mathbf{0}\mathbf{°}}$?

Short answer

The separation between two slits is${}^{1.22\text{'}{10}^{-8}\mathrm{m}}$.

Step-by-step solution

Given data

The wavelength of the orange light is ${}^{\lambda =610\mathrm{nm}\left(\frac{{10}^{-°}\mathrm{m}}{1\mathrm{nm}}\right)=6.1\times {10}^{-7}\mathrm{m}}$

The angle for the first maximum is ${}^{30.0°}$

Finding the separation between two slits

A formula for the angle of the first-order maximum can be expressed as,

$\mathrm{dsin}\mathrm{\theta }=\mathrm{\lambda }$………………………….(1)

Substituting the given data in equation (1), we get,

$$\begin{gathered} d\times \sin \left(30.0°\right)=6.1\times {10}^{7}m \\ d=\left(\frac{6.1\times {10}^{7}m}{0.5}\right) \\ d=1.22\times {10}^{-6}m \end{gathered}$$

Thus, the separation between two slits is ${}^{1.22\text{'}{10}^{-6}\mathrm{m}}$.