Question

What is the effect on the interference pattern in Young's double-slit experiment when (i) the source slit is moved closer to the plane of the slits, and (ii) the separation between the two slits is increased? Justify your answers.

Hint:

The sharpness of interference fringes depends on the relative distances between the source, slits, and screen. Adjusting these distances changes the fringe spacing.

Answer 1

(i) As the source slit is moved closer to the plane of the slits, the sharpness of the interference pattern decreases. This happens because the light from different parts of the source overlaps and the fringes begin to blur, eventually disappearing if the slit is moved too close. The fringe sharpness is affected by the ratio \( \frac{s}{d} \), where \( s \) is the distance between the source and the slits, and \( d \) is the separation between the slits. If \( s \) decreases, the sharpness of the interference pattern decreases. (ii) As the separation between the two slits increases, the fringe spacing \( \beta \) decreases. The fringe spacing is given by: \[ \beta = \frac{\lambda D}{d}, \] where \( \lambda \) is the wavelength of light, \( D \) is the distance from the slits to the screen, and \( d \) is the slit separation. As \( d \) increases, \( \beta \) decreases, and the fringes become closer together.