Prism Spectrometer Objective: Optics Question

[doofus]

I am playing with a basic prism spectrometer for fun, and because a lot of design about these spectrometers has gone to the void over the years. As simple as this system is, my optics knowledge is ancient, and I have, unexpectedly encountered a puzzle. The set up is the following:

Linear path:
White LED -> 2mm tall x 100um wide slit -> planoconvex collimating lens (60mm focal length) -> Equilateral triangular glass Prism with a circumradius of ~2.5cm.

The incident angle of the collimated beam is roughly 70 degrees from normal on one of the prism faces.

The light refracts through the prism, thanks Snell, and if I follow its path with an index card I see a spectrum of colors emerge out the other face. I understand that on the screen what I am seeing is the overlap of the collimated beam at many wavelengths slightly offset from one another in space, but never the less each wavelength is overlapping with those nearby it.

Now what I've been told, in many old textbooks, is if I place a lens in the path of these refracted beams I will be able to image the diffraction slit, but the superposition of all of the wavelengths will remain spatially separated. Meaning I will obtain a spectrogram, which has less overlap of light intensity from the refracted beams.

In practice I do not obtain this result. As I move my screen from the lens to it's focal point I watch the rainbow of colors collapse into an image of the original slit? That is to say, there is no spectrogram, only white light in a shape and size which is highly similar to the original slit. As I go further from the focal point I again observe a rainbow image, but it grows out of focus. Why might I not see a "resolved" spectrogram in the focal plane? Is there a way to increase the horizontal size of the "resolved" spectrogram?

 

[phyzguy]

Something like this should be what you want. Can you show a diagram of your set-up? Are the lenses at the proper distance to collimate and focus the beam?

 

[phyzguy]

I sounds like you might be imaging light from the slit that didn't go through the prism. You need an opaque screen surrounding the prism so the only light that gets to your detector is light that went through the prism.

 

[doofus]

Thanks for your help on this. My set up is nearly identical to the diagram you've drawn, just a larger incident angle on the prism. The light is collimated to about a meter in length with <1mm divergence in radius in the horizontal plane.

Something you said resonated. I reset the prism so that the beam goes through the widest path to try to increase the dispersion. Now I no longer observe the white light image of the slit, which is good, because that violated my understanding of physics. I think, and say without doing the math, that the issue is the corners of the prism are truncated flat, possibly to prevent fracture, and it is possible the beam I was observing came from one of those facets rather then the triangle face. Meaning I was focusing past the width of the cut corner of the prism, down to the slit itself?

Now I am going to try to magnify the spectrum with an additional planoconvex cylindrical lens placed before the screen. At the focal length of the final lens, the image is still quite small(4mm wide by 2mm high). If I could get 1cm in width that would be great but 7cm would be more entertaining. I doubt I have the lens for that sitting around. This project is a great refresher in basic optics. I highly recommend it for anyone looking to remember some of the principals.

 

[Gleb1964]

What is the slit orientation? The orientation of slit should be perpendicular to dispersion, right?

 

[doofus]

Correct, the slit image's longest dimension(4mm) is orthogonal to the dispersed image.

I revisited this issue and my original belief that light was escaping the cut edges of the prism is incorrect.

I can reproduce this effect if my objective lens is plano-convex. Biconvex* lenses do not focus the image back down to white light, at their focal length I see a well resolved nonlinearly dispersed spectrogram.

Thin lens equations don't explain this well, I wonder if the only explanation would be geometric ray tracing?

 

[phyzguy]

Do you mean biconvex lenses?

 

[doofus]

Do you mean biconvex lenses?

Yes sorry, coffee has not entered my blood-stream yet. I edited the above post.

 

[Gleb1964]

Your setup should work with a plano-convex or a double convex lenses. The plano-convex would be better option.
But because a single lens has to much aberration so the aberration blur is exceeding you dispersion separation. To be able to see a color separation you need to stop down your beam diameter to reduce aberrations blur. The image plane is strongly tilted, so to get the best sharpness I do recommend to tilt the image plane by about 32 degrees.

 

[doofus]

Cool software.

I see, so you think the effect is due to aberrations. Makes more sense then violating laws of physics. I could put an aperture before the collimating lens. Sad to see some light intensity go, it isn't very bright to begin with, but, I now see the issue in the physical sense.

Does this imply that the biconvex lenses have more aberrations which is why I can see the pattern, or is it the opposite? My understanding has been that planoconvex lenses have less aberrations than their biconvex counterparts. The difference could be that the biconvex lens is more shallow in shape.