# Measurement of Focal length with Laser beam

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1. Mar 12, 2016

### Alettix

1. The problem statement, all variables and given/known data
Hi!

I have lately come across some tricky experimental physics tasks, where no solution is given. Some of them involved parts where the focal lenght of a convex lens had to be measured with a laser. How do you do this?

2. Relevant equations
1/l + 1/d = 1/f (1)
where f is the focal lenght, l is the object distance and d the image distance)

M = d/l (2)
where M is the magnification

3. The attempt at a solution

First I thought that one should be moving a screen behind the lens looking for the distance at which the laser beem form a sharp image. At this distance equation 1 is valid . Because the beams from the laser are parallell, l = ∞ and therefore d = f.
However, trying this method out I quickly realized that with a so tiny "object" as a laser, the distance at which the image is the sharpest can not really be determined.

I tried to move the screen futher away and to some calculations from the magnification. But I guess that the formula for magnification is only valid at the image point as well, because this yield very weird results.

Could somebody please put me on the right track of how this kind of experimental task should be solved?
Thank you! :)

2. Mar 12, 2016

### Benoit

3. Mar 13, 2016

### Alettix

4. Mar 13, 2016

### Merlin3189

This Q has had me thinking. As yet I can't see any "laser" way of doing this. I thought maybe the physicists had some trick they could do here.

Anyhow, I didn't like the two parallel lasers as it did not look very accurate to me, though maybe I'm wrong - I'll have to try it.
My two thoughts are:
Just use it as a bright light. Put a spot on a screen and try to get an image of that spot on another screen, as you'd do with an ordinary lamp.
Use a diffraction grating (or CD - we don't need anything specific) to split the laser beam into two (& more) emanating from a single point. Use the lens to focus two of these reflected (or transmitted, with appropriate grating) beams to a single point. Since you are not looking for focus, just convergence, it should be easier to find the focal point.

Edit: just doing the sums and I think a CD would be too fine a grating, so you may have to get a proper grating, unless you know of something else.

Last edited: Mar 13, 2016
5. Mar 14, 2016

### Alettix

Thank you Sir, I think the spot on a screen might be the solution, although I am worried about the tiny diameter of the laser beam...

The problem description did not mention diffraction granting, so I assume that it shouldn't be used (these experimental problems are old ones from a physics competition, so if there is no diffraction granting in the description, the competitors were not allowed to use it). Also, the actual goal of the problem was to determine how well the formula:
f = nR/(2(n-1))
Describes the focal lenght of a spherical lens (with radius R and index of refraction n) as a function of deviation from the optical axis (where the formula is assumed to be true). This means that parallel beams cannot really be used, because they already deviate from the optical axis. Or am I wrong?