   # Young's double slit experiment

This experiment to use the effects of interference to measure the wavelength of light was devised by Thomas Young in 1801, although the original idea was due to Grimaldi. The method produces non-localised interference fringes by division of wavefront, and a sketch of the experimental arrangement is shown in Figure 1. Light from a monochromatic line source passes through a lens and is focused on to a single slit S. It then falls on a double slit (S1 and S2) and this produces two wave trains that interfere with each other in the region on the right of the diagram. The interference pattern at any distance from the double slit may be observed with a micrometer eyepiece or by placing a screen in the path of the waves. The separation across double slit should be less than 1 mm, the width of each slit about 0.3 mm, and the distance between the double slit and the screen between 50 cm and 1 m. The single slit, the source and the double slit must be parallel to produce the optimum interference pattern. Alternatively a laser may be used and the fringes viewed on a screen some metres away without the need for a micrometer eyepiece or a single slit.

The formula relating the dimensions of the apparatus and the wavelength of light may be proved as follows. Consider the effects at a point P a distance xm from the axis of the apparatus.

The path difference at P is S2P - S1P.

For a bright fringe (constructive interference) the path difference must be a whole number of wavelengths and for a dark fringe it must be an odd number of half- wavelengths (Figure 2).
Consider the triangles S1PR and S2PT.

S1P2= (xm – d/2)2 + D2 S2P2 = (xm2 + d/2)2 + D2

Therefore:

S2P2 – S1P2 = 2xmd so (S2P - S1P)(S2P + S1P) = 2xmd

But S2P + S1P = 2D

within the limits of experimental accuracy for D would be at least 50 cm while d would be less than 1 mm making the triangle S1S2P very thin.
Therefore: S2P – S1P = xmd/D

For a bright fringe:     ml = xmd/D

For a dark fringe:     (2m + 1)l/2 = xmd/D

Where m = 0,1,2,3 etc. and so the m th bright fringe for m = 3 is 3lD/d from the centre of the pattern
The distance between adjacent bright fringes is called the fringe width (x) and this can be used in the equation as:

Wavelength (l) = xd/D

Fringe width (x) = lD/d

Note that the fringe width is directly proportional to the wavelength, and so light with a longer wavelength will give wider fringes. Although the diagram shows distinct light and dark fringes, the intensity actually varies as the cos2 of angle from the centre.
If white light is used a white centre fringe is observed, but all the other fringes have coloured edges, the blue edge being nearer the centre. Eventually the fringes overlap and a uniform white light is produced. The separation of the two slits should be of the same order of magnitude as the wavelength of the radiation used.

Example problem
Calculate the fringe width for light of wavelength 550 nm in a Young's slit experiment where the double slits are separated by 0.75 mm and the screen is placed 0.80 m from them.
Fringe width (x) = lD/d = 550x10-9x0.80/0.75x10-3 = 5.9x10-4 m = 0.59 mm