[Case Study — Young's Double Slit Experiment]

The principle of superposition is used to understand the phenomenon of interference of light waves. It states that at a particular point, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each wave. Thomas Young devised a way to obtain two coherent sources using two identical pinholes ($S_1$ and $S_2$) illuminated by a single monochromatic pinhole source S. The pattern consists of alternate bright and dark fringes. The fringe width depends on the distance between $S_1$ and $S_2$, the distance of the screen from the plane of $S_1S_2$, and the wavelength of light used.

Q.IV. In a Young's double slit experiment, the slit separation is 0.8 mm and the interference pattern is obtained on a screen kept 50 cm from the plane of the slits $S_1$ and $S_2$. If the first bright fringe is formed 0.4 mm from the central maximum, the wavelength of light used is: