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The following YouTube video from Sixty Symbols ( What is the maximum Bandwidth? - Sixty Symbols https://www.youtube.com/watch?v=0OOmSyaoAt0 )states that only a laser which always shines truly shines as a single frequency (df = (or ~=) 0). A laser which is active only long enough to send a good pulse of coherent light must contain all of the frequencies necessary to shorten that pulse, where df * dt =1. No need to mess with the frequencies present -- the nature of the thing will ensure that sufficient distribution of frequencies are present.
If I shine a laser pulse through a prism, intuition says that I still only get a single spectral line coming out. Is this consistent? Is my intuition wrong, and the pulse of coherent light will spread through the prism? Will there be spreading only at the start and end of the pulse, but sufficient? To my level of knowledge, this is not a duplicate of:
Light of a specific wavelength going through a prism
It is related related to this question, sprung from the same YouTube video:
Does switching a laser on create multiple frequencies?
And it may well be answered here, but I am not conversant in compact support and so forth:
Does switching a laser on create multiple frequencies? Finally, can it be answered without resort to quantum superposition? This answer may well be what I am looking for, but that is not at all evident from my ability to read it:
Frequency Chirp, Instantaneous Frequency and Photons

My question therefore is limited to the observable behavior of a pulse and a prism. Will I observe any spectral spreading of a laser pulse through a prism due to the requirements of df * dt = 1?

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Yes, since laser pulses with finite temporal length also have a non-zero spectral width, a dispersive prism will cause a laser beam to spread out, with different wavelengths emerging from the prism at different positions and angles. This spread will occur throughout the pulse, not just at the beginning and end, as all spectral components are present at all times.

For a continuous-wave laser (like a laser pointer) or a laser producing pulses of, say, a few picoseconds or longer, this dispersion will typically be small and invisible to the naked eye. Nevertheless, it is an important and useful effect, as prisms or diffraction gratings can be used to separate out part of a laser spectrum to make a more monochromatic beam.

For very short laser pulses of a femtosecond or less, the frequency spread is enormous. Here is an image of a type of laser called a frequency comb with its spectrum spread out (not using a prism, but the principle is the same) onto a piece of paper, showing that it spans almost the whole visible range. frequency comb

The Wikipedia article on mode locking of lasers has a useful animation (by Davidjessop) showing how standing waves of different wavelengths can add together to create a traveling pulse of light: Mode-locked laser animation

I can't tell from your question whether you are already familiar with Fourier transforms, but if you want to understand more about why $\Delta f$ is inversely related to $\Delta t$, that would be a good place to start!

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