Question

Derive condition for occurrence of dark and bright fringes on screen in young’s double slit

interference experiment. Define fringe width and derive formula for it.​

Answer 1

Answer:

These conditions show that the bright and dark fringes (or bands) occur alternately and are equally spaced. For Point O', the path difference (S2O' - S1O') = 0.

Answer 2

Answer:

Thomas Young convincingly demonstrated the light wave interference in 1801. He shone light through two closely spaced side by side pinholes. He found that the light recombines to produce fringes of brightness and darkness on a screen behind. The bright fringes were formed when a crest of the light wave through one hole meets the crest from the light through the other hole. Both the waves arrive in phase at the screen. The dark fringes were formed when a crest from one wave meets a trough from the other.

Consider a monochromatic source being placed at a certain distance such that it is at the same distance from the two slits

and

so that they act as two coherent sources. The arrangements are as shown in the figure. Interference patterns are produced only when light passes through both the slits. Consider the two approximations in the experiment.









According to these conditions, there is a path difference that results in dark and bright fringes on the screen.

Bright fringes are formed when there is a maximum intensity at point P. That is the path difference is





Thus the position of the

fringe is,





Dark fringes are formed when there is minimum intensity. That is,





Thus the position of the

fringe is,





The distance between two adjacent dark or bright fringes is called the fringe width







Explanation: