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In an experiment I conducted I used a spectrometer to find the spectrum of green laser and green led.

this is what I found:

LED spectrum: LED spectrum

Laser spectrum:

enter image description here

why is the spectral width of the LED is wide compared with the laser?

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In short, because they produce light using completely different mechanisms. In fact, the light produced in a green laser is actually frequency-doubled infrared light (which is part of why cheap green laser pointers that don't properly filter out the leftover infrared light are dangerous).

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Also there are green lasers that produce light directly from semi-conductor materials (InGaN -see wiki). The green LED uses the same material but probably less pure. The laser is a tiny chip ( very pure, very few crystal defects, very carefully grown) with mirrors at either end. Due the exact dimensions of the crystal and distance between the mirrors a narrow range of optical frequencies is produced. An LED is a bigger device with no mirrors and light scatters out.

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The spectrum of the laser is much more narrow due to the fact that optical gain of the laser only occurs at the resonant wavelengths of the optical resonator used in the laser.

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