# Optics, laser beam focusing

1. May 5, 2014

### Matt atkinson

1. The problem statement, all variables and given/known data
In an experiment a laser beam is focussed on a sample by a lens. The sample has micro structures spatially separated by 5 microns. In the experiment, each micro-structure has to be studied individually using the laser, so that illumination of two or more adjacent micro-structures must be avoided. If the laser wavelength is 632 nm and the diameter of the beam is 1 mm, find focal lengths of the lens suitable for this experiment.

2. Relevant equations
I have no idea.

3. The attempt at a solution
I assumed that the spot sized needs to be focussed to >5 microns so it meets the requirements.
but I really have no idea.

2. May 5, 2014

### BvU

Time to generate an idea, isn't it? Apparently the parallel beam isn't going to be focused to a zero diameter focal point. What can be the reasons for that ? Why do they tell you the wavelength ?

Is there any context for this question ? Did you learn anything recently that might apply here ?

3. May 5, 2014

### Matt atkinson

I Learnt about the Rayleigh criterion recently, I wonder could that apply.
d/l>1.22*lambda/D
l=f?
But, I'm not quite sure how it could apply.

4. May 5, 2014

### BvU

So you google Rayleigh criterion, get an article on angular resolution. The 1.22 appears to come from the diameter of the first minimum of the Airy disk: diffraction limitation! Follow the link and it even has a small section on focusing a laser beam!

Huijgens' principle states every point of the 1mm laser beam aperture is point source for waves that propagate in all directions. All the stuff that expands sideways effectively interferes itself away, only straight through adds up constructively. (Not even that is true: a laser beam has some minute divergence).

In the focal plane of the lens you get a diffraction pattern that is the fourier transform of the aperture. Circular aperture -> Airy disc.

So yes, this is a nice relevant equation. Fill in the numbers to get l < a very small number.

No wonder if you want to distinguish something of dimensions 8 times the wavelength. And this very small number is a genuine upper limit, which you want to stay away from as much as you can! Use bluer light, or start saving for an electron microscope: $\lambda$ of the order of 10-5 x visible light!

5. May 5, 2014

### Matt atkinson

oh wow, thank you so much.
I have been trying to do it for a while, and didn't fully understand my notes, I tried google but porbably didnt search the right things.
I think I understand now.
Thanks BvU