Question

In a single-slit diffraction experiment, what must be the ratio of the slit width to the wavelength if the second diffraction minima are to occur at an angle of 37.0° from the center of the diffraction pattern on a viewing screen?

Short answer

The ratio of slit width and wavelength is 3.33

Step-by-step solution

Identification of given data

The given data can be listed below,

• The angle of diffraction minima is,$\theta =37°$
• The order of the diffraction minima is,$m=2$

Concept/Significance of single slit diffraction

When light passes through a single, narrow slit and comes to rest on a plane at a great distance from the slit, this is known as diffraction.

Determination of the ratio of the slit width to the wavelength

The brags law of diffraction is given by,

$$\begin{gathered} a\sin \theta =m\lambda \\ \frac{a}{\lambda }=\frac{m}{\sin \theta } \end{gathered}$$

Here,$\lambda$ is the wavelength of the light, ais the slit width, m is the order of diffraction minima.

Substitute all the values in the above,

$$\begin{gathered} \frac{a}{\lambda }=\frac{2}{\sin 37°} \\ =\frac{2}{0.601} \\ =3.33 \end{gathered}$$

Thus, the ratio of slit width and wavelength is 3.33.