You have two diffraction-limited laser b eams with different wavelengths (lamba 1) and (lambda 2) incident on a lens of focal length f, and you want the beams to focus to the same size spot. How would you accomplish this?
I think it has to do with either varying the starting diameter of the beam or varying the incident angle, but i'm not sure. Anyone have any insight on this? d = [(lambda)f]/[(pi)D]
Sure, there are several ways to do this. The spot size is basically given by the uncertainty principle x p >= hbar/2. But x is the spot size and p is the photon momentum. If we assume to two beams with the same width before the lens, but different frequency, then p will differ by the frequency, so x has to differ as well. Now, p for a photon depends on the energy of light (frequency, wavelength, or however you want to measure it) AND the direction. So if you want the same spot size (the same X) you need to change the direction of the rays of the photons. So you need to change the incident angle, which basically means you need to change the diameter of the incoming beam. A larger beam focused to the same spot size, will have a larger range of angles, so a larger range of momentums. But you already said that.
You could also change the angle. If you assume a beam that is not collimated, but is converging or diverging, it too will have a different spot size from a collimated beam. You said that too!
And I can think of a third way to do that, too. All materials, in practice, are dispersive, meaning they have different indices of refraction. That means a lens made with that material will bend different wavelengths by different amounts. So you could pick a special material that has a specific ratio of indices of refraction for the two wavelengths, such that the spot size for both beams are the same, despite the wavelengths difference. In practice, this probably will not be possible, but in theory, ti's an option!
Those are the 3 ways I can think of to get your desired result. But not, the focus will probably not be in the same plane!
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Stupid second law of thermodynamics got nothin on us - Help me figure out how to do something impossible?
All I wanna do is re-collimate a diffuse laser reflection...
35 mW of very green laser light shining on a small white plastic object is BRIGHT. The light seems readily-enough gathered with a large objective lens, but I get hung up there time and again.
Should I be using smaller gathering lenses and/or pinhole optics in some way?
Or hell, am I better off trying to gather the light with some sort of convex mirror?
Note: my desired gathered/focused/collimated output does not need to be a tiny beam - in fact, a beam with some surface area is preferable.
Can this be done with standard optics?
Good point, first poster - I have resigned myself to losing a lot of my original energy. My basic goal is to collimate my reflection well enough to be able to beam it through a beamsplitter and/or homemade interferometer
There are non-focusing optics that will concentrate diffuse light.
But really, without knowing the application it is pretty difficult to suggest the best strategy.
What does your problem have to do with thermodynamics? It seems the (except for being very complicated) you have not done anything irreversible by scattering the light.
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