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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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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.

This would spoil your wavelength discrimination, contradicting the whole purpose of a diffraction grating.

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  • $\begingroup$ But what if we formed an image right at the grating? Would the conclusion be the same? $\endgroup$
    – Bidon
    Mar 22 at 20:28
  • $\begingroup$ How do you form an image unless the rays are not parallel? $\endgroup$
    – ProfRob
    Mar 22 at 20:30
  • $\begingroup$ Yeah that makes sense $\endgroup$
    – Bidon
    Mar 22 at 20:31
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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.

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.

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  • $\begingroup$ The problem is that, after the rays diffract, you'll want to focus them to resolve the spectrum. But if your incident rays aren't collimated, the diffracted ones will be unfocusable—even for a monochromatic point source, even by an ideal lens. See my question for a ray diagram showing this problem. $\endgroup$
    – Ruslan
    Mar 23 at 22:44
  • $\begingroup$ @Ruslan, In your drawing, if the lens is placed on the grating, a focused spectrum will form at a distance beyond the lens as calculated by the Lensmaker's Equation using the slit-lens distance and the focal length of the lens. If the slit is too close to the lens, the aberrations will be bad of course. I would use a plano-convex lens and an incoming beam that doesn't spread more than about 5 or 10 degrees total. $\endgroup$
    – S. McGrew
    Mar 24 at 0:36
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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.

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  • $\begingroup$ A beam from a point source is not collimated, but is easily re-formed into a collimated beam by a lens. If the lens is one focal length from a white light source, and the grating is right against the lens, the lens sees a string of monochromatic point sources along a line in the back focal plane and focuses them at infinity along a line. A bit of adjustment puts the focused spectrum where you want it. Trivial to do at home. $\endgroup$
    – S. McGrew
    Mar 24 at 0:41
  • $\begingroup$ 40-plus years in an optics lab teaches one a few things that aren't necessarily obvious. $\endgroup$
    – S. McGrew
    Mar 24 at 0:46

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