# Explain briefly about monochromatic light. Is it really possible?

Charlie Hooper | (Level 2) Educator

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Monochromatic light is light of a single frequency. If the concept is taken seriously, that means that a monochromatic light takes the form of a time dependent sinusoidal function that stretches infinity into the past and infinity into the future. For instance, for a classical monochromatic light wave of angular frequency `omega` traveling in the z-direction in the cartesian coordinate system, it takes up the form:

`E(z,t)=E_0Cos(kz-omega t+sigma)` in the x-direction

`B(z,t)=E_0/c Cos(kz-omega t+sigma)` in the y-direction

If you don't recognize the constants, don't worry about it. Just notice if you plot these functions with respect to time, they are infinite. This does not agree with our universe which has a finite amount of time.

What actually tends to happen is when we talk about making "monochromatic" light in the lab (a localized part of space) there is an inherent uncertainty in the frequencies of the light due to its quantum nature. If we turned on a laser and then turned it off how do we represent this if our monochromatic light equations are infinite in time? In fact, we can represent this burst of light as a wave packet.

wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit

Moreover, the narrower the spatial wave packet, and therefore the better localized the position of the wave packet, the larger the spread in the momentum of the wave. This trade-off between spread in position and spread in momentum is a characteristic feature of the Heisenberg uncertainty principle

The momentum (`P` ) of light is related to its frequency (`f` ) by `P=(hf)/c` . So an uncertainty in its momentum is proportional to the uncertainty in its frequency.

We can get very close to pure monochromatic light with lasers and filters, but there is always a certain small spread in frequencies. Although, there are techniques to refine this spread to get almost pure monochromatic light. To get the best quality monochromatic light requires using "light amplification by stimulated emission of radiation" (laser) action in conjunction with an optical cavity to further filter the light.

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