Question

State the conditions of interference of light. Obtain the expression for the fringe width in Young's double slit experiment.

Hint:

The fringe width in Young’s experiment is directly proportional to the wavelength of the light and the distance to the screen, and inversely proportional to the slit separation.

Answer 1

Step 1: Conditions for Interference of Light.
For interference to occur, the following conditions must be satisfied: 1. The light sources must be coherent, meaning they must have a constant phase relationship. 2. The light waves must have the same frequency and wavelength. 3. The waves should propagate in the same direction, ideally with a constant path difference.
Step 2: Expression for Fringe Width.
In Young's double slit experiment, the fringe width \( \beta \) is given by the formula: \[ \beta = \frac{\lambda D}{d} \] where: - \( \lambda \) is the wavelength of the light, - \( D \) is the distance between the slits and the screen, - \( d \) is the separation between the slits.
Step 3: Conclusion.
Thus, the fringe width \( \beta \) in Young's double slit experiment depends on the wavelength of the light, the distance between the slits, and the distance from the slits to the screen.