# Can light have zero wavelength?

As you increase the energy of a photon it's wavelength shortens. Is it theoretically posible for light to not have a wavelength? Like a still pond?

• Perhaps you could say that a motionless magnet or point charge gives off light of zero wavelength. Then again, perhaps not. Nov 29 '15 at 9:03
• Possible duplicates: physics.stackexchange.com/q/16391/2451 and links therein. May 8 '17 at 20:10

The relationship between energy and wavelength:

$$E = h f = \frac{h c}{\lambda}$$

As $\lambda$ goes to zero, $E$ goes to infinity.

So "no".

In case of photon's wave nature they have definite wavelengths for definite energies. If wavelength become zero then its energy become infinite which is impossible. Secondly, every wave must have wavelength which defines its motion. If wavelength become zero then wave become motionless.

• I guess you cannot argue with the maths but it does seem odd to me that the lowest energy state of light would require infinite energies. Seems like it's upside-down Nov 30 '15 at 18:15
• @Justin Why are you saying the lowest energy state of light has infinite energy? The lowest energy state of light is an infinite wavelength corresponding to zero energy. Obviously a state with infinite energy is not the state with lowest energy. Sep 19 at 17:24

How about doing it the other way? Quote "The earth is a magnet, and it is accelerating as it rotates the Sun, so it radiates EM waves with a period of 365 days and a wavelength of 1 light year." The frequency would be so low as to have no detectable wavelength. Like a still pond.

• Welcome on Physics SE :) I think it would be nice if you could elaborate on your answer a bit - as of now, it is hard to really tell what you might be thinking about. May 8 '17 at 21:01

A still pond would be equivalent of infinite wavelength and the frequency of 0. The equivalent of 0 wavelength would be an infinitely tall tsunami wave in the pond. It is not possible to have wavelength at exactly 0, but you can get arbitrarily close to 0. Proof: any positive non-zero wavelength, no matter how small, can be made smaller via blueshift (approaching towards the source). At some point, though, you will be limited by the amount of energy needed to gather in order to create such radiation.