Chapter 19, Problem 33A

To determine

To explain:The procedure to use a light of known wavelength for obtaining the distance between two narrow slits.

Answer to Problem 33A

The wavelength of the light source can be used TO-DETERMINE the distance between the two slits in double slit experiment.

Explanation of Solution

Introduction:

The double slit experiment is used to show that the light and matter can exhibit both the particle and wave characteristics. The double slit experiment can be used to measure the wavelength of the light source.

Consider the light from the source falls on the double slits $S_{\text{1}}$ and $S_{\text{2}}$ creating interference pattern which in turn fall on the screen.

The demonstration of the double slit experiment is shown in the figure below.

  

Consider the distance between the two slits $S_{\text{1}}$ and $S_{\text{2}}$ is denoted by $d$ .

Consider the screen is placed at a distance $L$ from the double slits.

The light from monochromatic light source falls on the double slits resulting in the formation of the interference pattern recorded by the screen.

The wavelength $\left(\lambda \right)$ of the light source depends on the phase difference between the waves coming out of the slits and reaching the screen.

The waves coming out of the two slits are in phase along the central point of screen and add ups constructively resulting in bright central band formation.

Consider the wavelength $\left(\lambda \right)$ of the monochromatic light used as source is known.

The distance $\left(d\right)$ between the slits can be determined using the relation:

  $d=\frac{\lambda L}{x}$

Here, $x$ is the distance between central bright band to the first bright band (measured in the screen).

Hence, the wavelength of the light source can be used TO-DETERMINE the distance between the two slits.

Conclusion:

Thus, the wavelength of the light source can be used TO-DETERMINE the distance between the two slits in double slit experiment.