Question

A double-slit esperiment is performed with light of wavelength 600nm. The bright interference fringes are spaced 1.8 mm apart on the viewing screen. What will the fringe spacing be if the light is changed to a wavelength of 400nm?

Answer 1

Concepts and reason

The concept used to solve this problem is fringe spacing in young’s double slit experiment.

First, find fringe spacing expression for light used.

Finally, use wavelength and spacing of bright interference fringes to find the fringe spacing for light used.

Fundamentals

Light ray passing through the two slits of double slit experiment will have phase difference which results in the interference pattern that is seen on the screen.

Constructive interference results in the increase in the amplitude of the resultant wave whereas destructive interference results in the decrease of the amplitude of the resultant wave.

The points of constructive interference will create white bands on the screen. And the points of destructive interference will create black bands. These black and white bands are called interference fringes.

Fringe spacing is defined as the length between any two consecutive bright or dark fringes.

The expression for fringe spacing is,

Here, the fringe spacing is , the wavelength is , the distance from slit to the screen is , and the distance between the slits is .

The expression for fringe spacing is,

The fringe spacing expression for the light is,

…… (1)

Here, fringe space for the light is and the wavelength of the light is.

The fringe spacing expression for the light is,

…… (2)

Here, fringe space for the light is and the wavelength of the light is.

Dividing equation (2) by (1),

The expression for the fringe spacing for light used is,

The expression of the fringe spacing for light is,

Substitute for , for , and for .

Ans:

Thus, the fringe spacing for light is.