Problems Based on Young's Double Slit Experiment - Angular Fringe Width

The wave nature of light is proved with the help of Young's Slit Double Experiment.

In Young's Double Slit Experiment there is a formation of a particular pattern on the screen.

This pattern is formed due to different intensities of light because of the interference of light.

There is also the formation of angular fringe width in Young's Double Slit experiment.

Now, we will learn about angular fringe width with the help of numerical.

Let's understand the concept with the help of numerical.

Let's consider that, in YDSE the angular width of a fringe formed on a distant screen is $1 °$ .

And the wavelength of light used is 6000 Angstrom. Then we have to calculate the spacing between the slits.

Now we have to find the distance between the slits.

So, we will proceed with the solution with the help of an angular fringe with formula.

In the YDSE, the angular fringe width is represented by $θ$ $_{1}$ and $θ$ $_{2}$ .

The formula of angular fringe width is given as,

So, the angle at which fringe width is formed is converted into radian.

The distance of the screen in radians,

Now for finding the spacing between the slits, we will put the value in the equation.

The calculation for finding the spacing between the slit is shown,

The value of spacing between the slits is given as,

Now, again consider a second numerical problem.

Now consider the situation, when we are using the sodium light in YDSE, of wavelength 5980 angstroms.

An angular width of $0.20 °$ is given and we have to find the wavelength when angular width will increase by 10%.

So, we have to find the value of wavelength for which formed width is $10 %$ greater than the previous wavelength.

So, let's start with the solution of the numerical.

First, we convert the given angle in the radians.

The formula of angular fringe width is given as,

Next, we will substitute the values in the angular fringe width formula to form a equation.

Now, we will form the new equation for finding the new wavelength.

The value of new angular displacement is,

Substituting the value of new angular displacement and forming new equation.

For finding the new wavelength we will equate both the equation.

The value of new wavelength is given as,

From the above numerical we have understood the concept related to the angular fringe width of YDSE.

The End