## Wednesday, January 28, 2015

### Fringe Width and Angular Fringe Width in Interference

Fringe width is the distance between two successive bright fringes or two successive dark fringes. In the interference pattern, the fringe width is constant for all the fringes. It means all the bright fringes as well as the dark fringes are equally spaced. We can derive the equation for the fringe width as shown below.

Fringe width is independent of order of fringe.

Fringe width is directly proportional to wavelength of the light used.

Hence fringe width for the red colored source is going to be greater than the fringe width of violet colored source.

If the interference experiment is conducted in the denser medium, the corresponding fringe width is reduced by its refractive index times. It means when the experiment is conducted in the denser medium we can observe that the fringes appear close to each other.

We can also define the angular fringe width as shown below.

In the interference pattern the bright spots and the dark spots are equally spaced. The path difference as well as the phase difference between any two successive bright spots or any to the successive dark spots is always constant. The variation of intensity of the output wave is regular and systematic as shown below.

Problem and solution

Two coherent sources are 0.18 mm apart and the fringes are observed on the screen 80 cm away. It is found that the fourth bright fringes 10.8 mm away from the central bright fringe. What is the wavelength of the light?

We know the condition for the constructive interference and the location of the bright spot on the screen. Using that formula we can find out the wavelength of the light as shown below.

Problem and solution

In the double slit experiment the slits are separated by 0.1 mm and they are at 50 cm from the screen. The wavelength of the light used these 5000 Å. Find the distance between seventh maximum and 11 minimum on the screen.

The formation of bright spots in the dark spots on the screen due to interference pattern is regular and systematic. We can apply the formula that we have derived for a location of the bright spot and the dark spot as shown below and solve the problem.

Related Posts