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In all of the images I've seen from a spectrometer, there's always a collimating element that places an image at infinity so as to have parallel rays hitting a diffraction grating. But why do we need that? I understand that the theory behind gratings is based on a plane wave hitting the grating, but if that were not the case, what implications would it have? I ask this because collimating a beam of light doesn't seem to be an easy task specially if the light source is something like an LED or a simple incandescent bulb, but that's another question, I suppose.

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2023310 — In simple thin-lens theory, without diffraction, any convex lens can be used to collimate light or transfer an image from one location to another.

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202194 — S is called the density matrix or coherency matrix associated with a polarized beam (a pure state in quantum mechanics). As we have seen already ...

I completely disagree with the answer by @ProfRob. If a beam is focused beyong the grating, it forms the focused image of a spectrum at the distance of the undiffracted focused beam. As long as the incoming beam has high spatial coherence, the wavelengths are well separated at that spectrum image. Of course aberrations can occur.

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A light prism is a transparent optical element with flat, polished surfaces that refract, or bend, light.

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When the direction of the incoming beam is changed the interference pattern also changes direction, hence a shift results on the screen. An uncollimated beam is an incoherent superposition of beams from different directions. The results is a convolution of shifted interference patterns, in other words the image will be blurred.

If the beam wasn't collimated then light with different wavelengths but from different parts of the source, arriving at different incidence angles, would be diffracted in the same direction.

20211127 — My textbook describes light as either s- or p-polarized or a mixture of both, depending on the orientation of the electric fields towards the plane of ...

When the electric field vectors are restricted to a single plane by filtration, then the light is said to be polarized with respect to the direction of ...

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The main reason a collimated beam is usually used to illuminate a grating is not that it's necessary; it is simply that it's simpler to visualize what's going on.