Question

A quasi-monochromatic beam of light illuminates Young's double-slit setup, generating a fringe pattern having a 5.6-mm separation between consecutive dark bands. The distance between the plane containing the apertures and the plane of observation is 10 m, and the two slits are separated by 1.0 mm. Sketch the experimental arrangement. Why is an initial single slit necessary? What is the wavelength of the light?

Answer 1

In Young's double-slit setup, an initial single slit is necessary as it acts as the source of light and allows diffraction. The wavelength of the light can be calculated using the separation between consecutive dark bands, distance between the slits, and the distance between the screen and the slits.

Step-by-step explanation:

To sketch the experimental arrangement for Young's double-slit setup, we have two slits (S1 and S2) that are equidistant from the main slit (So). The light from the monochromatic source falls on the main slit (So) and then passes through S1 and S2. The screen is placed at a distance D from the slits.

An initial single slit is necessary because it acts as the source of light and allows the light waves to pass through and diffract before reaching the two slits. This diffraction helps in creating interference fringes on the screen.

Wavelength of the light: Using the given separation between consecutive dark bands (5.6 mm) and the distance between the slits (1.0 mm), we can calculate the wavelength of the light using the formula for fringe separation: λ = (d * D) / w, where d is the separation between the slits, D is the distance between the screen and the slits, and w is the separation between the consecutive dark bands.