Many light sources like LEDs and lasers only emit a single wavelength of light.
Is there a light source that emits all wavelengths of visible light at the same time?
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Blackbody radiation for a white hot object emits the spectrum from infrared to ultraviolet.
Graphite is a decent approximation of a blackbody radiator. So graphite heated to white hot will emit the full spectrum of visible light.
Note however, that the spectrum will not be flat. There will be more energy on the ultraviolet end of the scale. See the curves in the graph on the upper right of the Wiki page for more information.
Sounds like you want a supercontinuum source:
Dear Gway, LED lights are a nice discovery but if you want a superior light that really emits at all frequencies, light bulbs with wolfram are a choice. They're cheaper, emit at all frequencies, don't contain Hg or other serious poisons, and another advantage is that they can heat up your home. Unfortunately, light bulbs are getting banned at many "progressive" places such as the European Union.
Black body radiation is nonzero at each frequency. It is an idealized radiation - which may be approximated by black objects (in the conventional sense). The most accurate natural source of black-body-like radiation is the cosmic microwave background but its temperature is 2.7 K. Black holes emit thermal Hawking radiation, too: but it hasn't been observed yet. However, the high frequencies carry a higher percentage of energy from a black body than the low frequencies. This can be circumvented by having a black body radiation from a whole array of sources that have different i.e. variable temperature. By taking a right mixture of the low-frequency ones, you may obtain a pretty much flat (or another sufficiently convex) spectrum over the visible (or another) interval as well.
If some light contains all frequencies, it is not coherent. Coherence requires the frequency - and usually the direction - to be universal for all the light. So the light containing all frequencies is pretty much by definition maximally incoherent. Coherence means that the information about the relative phases of the electromagnetic waves at two different points in spacetime is predictable and periodic. For light that contains all frequencies, it is unpredictable and aperiodic.
As far as I know, the wavelength of lights emitted by quantum dots depends only on their size. So we can tune the wavelengths by changing their size.
And then we can make a mixture of quantum dots of various sizes. These quantum dots can emit continuous spectrum, and provide color rendering index comparable with sunlight.
Incandescent lightbulbs can also generate continuous spectrum. But its color is yellowish, and its energy efficiency is too low.