A parallel beam of monochromatic light is used in a Young’s double slit experiment. The slits are separated by a distance d and the screen is placed parallel to the plane of the slits. Show that if the incident beam makes an angle with the normal to the plane of the slits, there will be a dark fringe at the center P of the pattern.

Question

Philoid · Accepted Answer

From the figure, we see a wavefront making an angle with the normal to the slit. One such wavefront is . also makes an angle . The path difference is given by the extra length .

From the figure and using trigonometry in , right angled at ,

For a dark fringe, the path difference should be

Hence,