The Maths of Youngs's Double Slit Experiment
Young's double slit experiment, along with the pattern formed on a screen, is illustrated below.
We can derive an expression for the distance between successive slits in two different ways. Both use the fact that for a bright fringe, constructive interference needs to occur, so the path difference for light from the slits needs to be a whole number of wavelengths.
Method 1 (no screen used)
Simple trigonometry gives the path difference above asand by equating this toa whole number of wavelengths, we obtain
Method 2 (screen used to show the fringes)
If a screen is used to show the fringes, the the rays from the slits cannot be parallel, else they would never meet and interfere, but they can be very close to parallel if D>>d.
From the diagram above, for smallso
If light of wavelength 500 nm is incident on slits 0.1 mm apart and the distance to the screen is 3 m, find the fringe separation.