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I have read that colored LED lights are nearly monochromatic. Does this mean that they could be used in double slit interference?

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The typical FWHM linewidth of a an LED is given by

$$\Delta{}\lambda= \frac{\lambda^2}{hc}3kT$$

The $3kT$ comes from the uncertainty of the initial and final energy levels of the carrier transitions generating the light, due to their thermal excitation. This works out to about 27 nm in the red region, for example. By comparison, a laser source can easily have a linewidth below 1 nm.

For the double slit experiment to work, the light travelling through the two slits to the dark regions on the screen must be coherent so as to produce destructive interference. Roughly, the path length distance must be less than the coherence length of the source. The coherence length is given by

$$L_{\mathrm{coh}}=\frac{c}{\pi\Delta\nu}$$

(For this case, the value is only approximate, since the formula assumes a Lorentzian line shape, which isn't what the LED produces)

In terms of wavelength,

$$L_{\mathrm{coh}}=\frac{\lambda^2}{\pi\Delta\lambda}$$

Continuing our example with red ($\lambda=650\mathrm{nm}$) light with 27 nm linewidth, this gives a coherence length of about 5 microns. Since the first fringe is formed when the path length distance is 1/2 wavelength, and this is substantially less than the coherence length, we should expect to see the first and maybe a couple of further fringes. We shouldn't expect to see dozens of fringes like we might see when using a laser source.

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