Lens Calculations to Focus Light

[AxisCat]

I am looking for help getting started with focusing light into my monochromator. This is all just hobby level stuff with limited budget for high end lab gear. I have a 35mm slide projector I am going to re-task as a light source. It has a 200 watt tungsten bulb that is passed through a collimating lens. My thoughts are to then pass the collimated light through a lens to focus it onto the entrance of my monochromator. The end goal being to increase throughput as much as possible.

Can someone point me in the right direction to equations that can help me predict what focal length lens would be required based on the distances on both sides of the lens? Or am I approaching this wrong??

 

[DaveE]

http://labman.phys.utk.edu/phys222core/modules/m8/thin_lenses.html
https://www.khanacademy.org/science/physics/geometric-optics/lenses/v/convex-lenses

Plus about a million other links on this subject if you don't like these.

 

[DaveE]

It may be as simple as just changing the distance between the lamp and the collimating lens. This is what the focus adjustment on the projector does.

 

[Drakkith]

Can someone point me in the right direction to equations that can help me predict what focal length lens would be required based on the distances on both sides of the lens? Or am I approaching this wrong??

If the light is collimated, then a lens of any positive focal length placed at any distance will bring the light to focus. But what you really want is to match the focal length with the physical distance you have available. A lens with a focal length of 50mm will bring the light to focus 50mm past the lens, for example. So if you want your collimator X distance from the lens, get a lens of X focal length. Note that this only works if the light is already collimated.

 

[AxisCat]

I appreciate the help and it seems I was making this way too complicated. I was trying to apply my experience as an amateur photographer to this. This projector looks like a classic example of the thin lens equation in the links provided by DaveE. I didn't mention the fact that this projector did come with a 124mm lens to focus the light. So the light train is composed of a the lamp, then the collimating lens, then the actual 35mm slide and finally the 124mm single element lens some distance away from the slide. Playing with the math it makes sense and explains why you must invert the slide too!

But I am not trying to form an actual image from one side of the lens to the other so none of this really applies. Like Drakkith says I just need to position my monochromator 124mm from the lens and that is the best I can do. I think I was confusing 'focusing' an object with a lens onto a plane with just 'focusing' or 'converging' the light down to the smallest area possible. If that makes sense?

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[Drakkith]

I think I was confusing 'focusing' an object with a lens onto a plane with just 'focusing' or 'converging' the light down to the smallest area possible. If that makes sense?

Those are the same things. The light from an object will form a sharp image when the image plane coincides with the focal plane of the lens.

 

[DaveE]

I think I was confusing 'focusing' an object with a lens onto a plane with just 'focusing' or 'converging' the light down to the smallest area possible. If that makes sense?

Those are the same things. The light from an object will form a sharp image when the image plane coincides with the focal plane of the lens.

Both of these statements confuse me. Although I'm sure we all understand the lens equation.

If your object is a point source, then it's image will also be a point. If it has some size, like the length of a lamp filament, then the image size depends on the magnification.

If your incident light is collimated, that is the same as a source infinitely far away, and the image plane will be the focal plane. Otherwise, the image plane is not the focal plane.

 

[Drakkith]

If your object is a point source, then it's image will also be a point. If it has some size, like the length of a lamp filament, then the image size depends on the magnification.

Certainly. But I'm not sure I understand what you're trying to get at.

If your incident light is collimated, that is the same as a source infinitely far away, and the image plane will be the focal plane. Otherwise, the image plane is not the focal plane.

Indeed. I guess I should have clarified that I was just referring to the OP's setup with collimated light. The focal point/plane of the lens is not generally located at the image plane. Only when the incoming light is collimated will that occur.

 

[AxisCat]

Again I want to thank you two for the help. I got lucky and the light from my projector nailed the entrance to my monochromator without any shimming in elevation of either piece. I ended up replacing the stock lens with a 24mm SLR camera lens and it did a very nice job focusing the light down to the entrance diameter I needed. And it did form a sharp image of the slide gate, the rectangular opening where the 35mm slide would sit. Once I get my photodiode sorted out I can start playing with things. I hope I can reach out in the future if I need assistance as get deeper into this project.

 

[varutmarius87]

Colimated light = parallel beam => the lens will focus the all the rays parallel with its optical axis into the focal point.

 

[AxisCat]

Colimated light = parallel beam => the lens will focus the all the rays parallel with its optical axis into the focal point.

Thanks for the reply. I am up and running light through my monochromator now. I am in the process of learning about photodiodes and transimpedance amplifiers. Do you have any experience with this?