[Johann Mahne]

Johann Mahne  asked the Naked Scientists:
   Hi Chris,

If two photons travel in parallel through the magnifying glass, one through the center and one through the outer perimeter, what causes the photons  to change their path through a magnifying glass?

Would the point where they meet (focal length) be affected by :
Their orientation with respect to each other?
Their wavelength?

What will happen at the focal point if:
They arrive in phase?Are photons able to combine to higher amplitudes,or are they only more closely packed together?

They arrive out of phase?Are photons able to annihilate one another?

If a giant magnifying glass was made.Could it be used to bend radio waves?

Regards
Johann
What do you think?

[sarujin]

If two photons travel in parallel through the magnifying glass, one through the center and one through the outer perimeter, what causes the photons  to change their path through a magnifying glass?

To use Richard Feynman's analogy: suppose you're a lifeguard standing on the side of a pool, and a beautiful girl is drowning in the pool away from you.

_You____________________
________________________
___________a_____b___c__
//////////////////////////////////////////
/////////water/////////////////////////
///////////////////////////////////girl//

Knowing that you can only run at a certain speed along the edge of the pool, and swim at a certain speed when in the water, where do you jump in?
a) the spot of least distance (a straight line to her)
b) the spot of least time of travel (a minimization of time elapsed)
c) the spot of least distance traveled in water

If you're a photon, then the fastest you can travel (on average) is the speed of light, which is a constant in air and water, and of course glass like in a lens. And photons take the path of least travel time (Fermat's principle) because such "stationary" paths offer the least amount of possible interference (this is complicated). So in other words light takes a bent path in glass because the speed of light is slower there.

Why is it slower there? Because the light is more readily absorbed by the atoms of glass, and the process of absorption and then emission takes a tiny bit of extra time.

Would the point where they meet (focal length) be affected by :
Their orientation with respect to each other?
Their wavelength?

Orientation absolutely affects it. If one of the photons is further out toward the edge of the magnifying glass (where it is thinner), then the amount of glass changes how long the light travels. However, if the lens has no "spherical aberration", then two photons will be perfectly focused to the same point no matter where they enter the lens.

Wavelength is also a crucial factor. The speed of light in a material can be dependent on the wavelength (or energy) of the photon, and this is described by the "dispersion" of a substance. Shorter wavelength (higher energy) photons often travel *slower* through substances than longer wavelength (lower energy) ones. Therefore a longer wavelength photon will be bent less.

What will happen at the focal point if:
They arrive in phase?Are photons able to combine to higher amplitudes,or are they only more closely packed together?

They arrive out of phase?Are photons able to annihilate one another?

If the photons are identical in wavelength, then they have the chance to "superpose" or "interfere". So, if they arrive in phase, the two photons have constructive interference and you see two photons. If they arrive out of phase (i.e. crest and trough aligning) then they have destructive interference and you see zero.

If a giant magnifying glass was made.Could it be used to bend radio waves?

In response to this final question, I'll give you a question. Suppose you have a parabolic dish, made out of not glass (I mentioned dispersion above; glass doesn't have much of an index of refraction for radio waves), but metal or some other substance. If you then put it on your roof, could it be used to receive signals from satellites around the earth and from outer space? If my crummy explanations don't satisfy you, go to the source and read a book about quantum electrodynamics, like QED by Richard Feynman.

[yor_on]

Very nice sarujin.

[Soul Surfer]

Just an addition.  It is possible to make "lenses" for radio waves that refract and create a focus by creating "artificial dielectrics".  These mimic the processes in atoms that create dielectric transparency by creating a light weight plastic foam support structure (a bit like expanded polystyrene) in which a small quantity of short (compared with the wavelength of the radio waves) thin metal wires are evenly and randomly distributed.  This then can be moulded or carved into a suitable lens shape to refract rather than reflect the radio waves.  This is used mostly in the microwave region because any longer wavelengths would require too large a physical structure.

[yor_on]

You could possibly consider it from experience too. We know that light will focus in a magnifying glass coming together into a point through countless experiments. Then the question becomes why it does so, and there 'principles' seems to play a very big part.

In a way it's not different from a photons 'geodesic' in space, it will in both cases use the path of no 'energy expended'. If we then look back on those paths we might by adding all possible paths it could have taken find some other way to express this fact, as Feynman did with his idea of paths interfering, some getting reinforced others quenched, until it in the end only exist one path, the one the photon took.

This universe seems very much to work on 'borders', defining what is probable or not to me.

[JP]

Feynman shmeynman.  Fermat figured this out in the 1600s: http://en.wikipedia.org/wiki/Fermat's_principle

[]

Ok, ok.  He didn't do it for photons, but rather for light rays.  Feynman realized that Fermat's principle works for light because it's a wave, so it should also work for quantum particles, which behave like waves. 

Yor_on: There is loose connection with geodesics, in a way.  Both involve calculating trajectories, from among all possible trajectories that minimize a quantity called the "action" in physics.  http://en.wikipedia.org/wiki/Least_action  But these paths don't have to be over curved space-time.  You can use the principle quite well to compute the motion of objects using Newton's laws.  It also happens to work in a wide range of applications in modern physics.

[yor_on]

Yes JP. That's my take too. It has to be a general principle of this universe, the path of least 'energy expenditure'.

[yor_on]

So

Here's a good question.

Why is it so?
And what is its implications?

[Johann Mahne]

sarujin

If my crummy explanations don't satisfy you

Your explanation seems good to me, thanks