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I recently came to know that two independent light sources can never produce coherent light waves for sustainable interference.The most common reason is because light waves are emmitted by billions of electron randomly and thus cannot be coherent.Now my doubt is, if we go by same reasoning then light waves from a single source as well should be incoherent being emitted by billions of electrons from atoms of same source(though I think it makes no difference).How can we account for this doubt?

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Now my doubt is, if we go by same reasoning then light waves from a single source as well should be incoherent being emitted by billions of electrons from atoms of same source(though I think it makes no difference).How can we account for this doubt?

It's usually true.

The light from an incandescent bulb or an LED is incoherent, and won't, for example, form strong interference fringes if you pass it through a double-slit apparatus. If you use a coherer, as mentioned in an answer to a previous question it's possible to obtain visible fringes from an incandescent source in the double-slit experiment.

Due to the small angular size of the sun when viewed from Earth, light from the sun has what is called spatial coherence (light at different positions on a plane transverse to the direction of propagation are coherent) but very little temporal coherence (light at different positions along the direction of propagation is not coherent). As such, you can form a double-slit interference pattern with it as discussed in a previous question, and as Thomas Young did, 150 years before the invention of the laser.

It's mainly when we talk about lasers that we get high degrees of temporal coherence. Lasers generate (most of their) light through the mechanism of stimulated emission. This means that the state of the emitted light is dependent on the light previously generated, so we no longer have the situation of light being emitted by billions of independent electrons. Instead we have the electrons interacting (through the light in the laser cavity) to produce coherent light. With temporally coherent light, we can not only see interference from the double-slit apparatus, but also in an apparatus like the Michelson Interferometer, which interferes a light beam with a delayed version of itself.

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