How does light spread beyond a cone?

[yonilite]

Hi!

I have a question and would greatly appreciate your help.

I've been wondering about how a light that is a emitted in the shape of a cone from a source (such as, a flashlight) can reach certain points outside the cone of light (although, much less intensly).

The simple answer you are probably thinking of is "well, the light is reflected from surfaces inside the cone's area and then reaches other points in space". That raises a different question - what if all of those surfaces are black and theoretically do not reflect anything? Or another option - those surfaces have colors different than the ones seen outside the cone (for example, a red surface reflects and let's us see a white surface outside the cone).

To understand better what I mean, go here:
http://id.mind.net/~zona/mstm/physics/light/rayOptics/rayOptics1.html

Look at the pictures. Notice there are white areas outside the cone which still show? How does this happen?

I was once told this is because each ray of light actually leaks during its "motion". Each point along the ray of light emits smaller rays of light, at the expense of the primary one. Is this true?

Thank you very much,
yoni

 

[russ_watters]

I don't see any white areas outside the cone in either picture.

Light beams can spread out, however, if the light hits particles of dust or water in the air.

 

[yonilite]

White Areas...

The floor in the picture has a white and black wave texture on it. Notice you can see it even outside the cone of light.

I know about the dust particles, but what about an empty space?

 

[russ_watters]

The floor in the picture has a white and black wave texture on it. Notice you can see it even outside the cone of light.

That was done for clarity in the picture. It does not imply that the light is spreading out.

I know about the dust particles, but what about an empty space?

Well, we see light from galaxies billions of light years away, nearly unimpeded.

 

[FreeZin]

reflecction of light when it hits particles in the air?
may also be the diffraction of light? (ie when it passes between e small amt of space between particles?)

 

[ooberchicken]

This could just be a setup of the render mode of the modeling program used. There could be extra lights out side the picture to illumante the flashlight, or maybe some other shading method. Most renderers base there graphical extrapolations on physics based simulations such as ray-tracing, yet the paramaters of the simulations can be changed to unrealistic values to acheve a more asthetic effect.

 

[russ_watters]

Yes, it is something like that. Most renderings - even before you add lights - start with a certain amount of flat light so you can see what it is that you are working on. Otherwise, you'd have a hard time understanding this picture - there'd be nothing in it besides the beam of light!

 

[phoenix5002]

There would be no light outside the cone if the image was rendered with no additional lights. However I still understand basically what your asking, although that image doesn't illustrate it. For another example, if you were to shine light through a tiny hole and no other light got out, the light through the hole would NOT continue in a perfectly straight line, it would also spread out in a cone shape. Like in the pitcure I have attatched.
View attachment light.bmp

This is because of the wave properties of light, and although your image or mine doesn't show it, there would be a larger dimmer cone of light outside the bright one, and this is for the same reason. I didn't show it because it would be really hard in paint, but the outter parts of the second cone of light would be very dim and there would be a bright beam in the middle

 

[russ_watters]

Yes, there would be diffraction, though the light would not spread-out evenly like in your picture. And it depends a lot on the size of the slit.

 

[yuiop]

Consider the design of a typical flashlight. About 50% of the light from the bulb filament is directed back towards a parabloic reflector which redirects the spherically diverging rays into a nearly parallel or narrowly divirging cone going forwards. The other 50% from the front of the bulb element never hits the reflector and simply spreads out in a much wider cone. More sophisticated lighting arangements such as those used in a photo studio add a hemispherical reflector in front of the bulb to try and get more of the light to be reflected off the rear parabolic reflector. Even this is not perfect as the design of the reflectors assume a point source whereas the bulb filament is usually a strip up to a centimeter long. Some of the light reflects off the internal glass surfaces of the bulb or off the stem of the bulb in unintended directions. All of these considerations make it nearly impossible to design a flashlight that emits a perfect cone or beam like a laser. This is compounded by the fact that normal incadescent light is not coherent like laser light and photons interefere with each other and diverge away from each other. (In a laser beam, all the photons are near enough the same wavelength and perfectly in phase with each other, minimising divergent interferance.)

Next, consider how you see the the objects illuminated by the cone. If the cone is shone at at the floor most of the photons are reflected forward away from you towards an opposite wall. Imperfections in the illuminated surface scatter light in random directions. Less than 1% of the photons emitted from the flash light happen to reflect directly off imperfections on the floor directly back to the pupils of your eyes allowing you to actually see the floor. The remaining 99% scatter around the room illuminating it indirectly.

If as you suggest the floor had a perfectly light absorbing black surface you wouldn't see the anything in the room and you wouldn't see the floor or the cone of light either, (except for reflections off dust in the air, which you also want to illiminate :)

So assuming you want to see the floor and assuming the practical limitations of designing a perfect cone light source it is a realistic simultion to have indirect illumination outside the main light cone path.

Of course you could always check this by using a real flashlight in a dark room

 

[JeffKoch]

This is compounded by the fact that normal incadescent light is not coherent like laser light and photons interefere with each other and diverge away from each other. (In a laser beam, all the photons are near enough the same wavelength and perfectly in phase with each other, minimising divergent interferance).

I'm not sure what you mean here, but remember that photons only interfere with themselves and not with each other. Photons from a light bulb do not "diverge away from each other" any more or less than other photons do.

 

[yuiop]

I'm not sure what you mean here, but remember that photons only interfere with themselves and not with each other. Photons from a light bulb do not "diverge away from each other" any more or less than other photons do.

OK, I stand corrected. I am still coming to terms with a single photon interfering with itself in the dual slit experiment and now I am learning that that photons can ONLY interfere with themselves and not with other photons. If the reason normal light inherently cannot form a stable parallel beam like a laser is not due to the fact that normal light is incoherant (as I was taught a LONG time ago), then what is the reason?

Can anyone shed any light on that?

 

[jambaugh]

I'm not sure what you mean here, but remember that photons only interfere with themselves and not with each other.

That is not all together true. Light quanta can interfere both individually and between one another. Otherwise electromagnetic heterodyning (getting a beat frequency by mixing two signals) would be impossible.

To be more accurate the distinction really cannot be made between the two processes. "Two photons" can be sliced into a pair in various different ways (Distinct quantum frames) and self interference in one may resolve as mutual interference in another.

 

[JeffKoch]

Light quanta can interfere both individually and between one another. Otherwise electromagnetic heterodyning (getting a beat frequency by mixing two signals) would be impossible.

Mmm, I'll have to think some more about that, but I'm not sure this isn't consistent with the concept of photons interfering only with themselves. Two signals implies two possible source frequencies, and if you don't try to isolate which frequency is associated with a particular photon then the two possibilities will "interfere" for each photon separately.

In any case, it's a useful concept, and explains for example the observation of interference patterns from multiple slits even when the source brightness is so low that only one photon at a time passes through the slit plane.

 

[jambaugh]

There is no need to invoke quantum mechanics for this issue. Diffraction issues will be the same whether you count photons or work the problem with classical electromagnetic waves and I think in this problem diffraction is not an issue. It all comes down to geometric optics.

Start with a finite width circular source behind a circular opening. You get two cones. Assume no reflectors and clean air. The inner cone is the cone inside which you can see the whole of the source. The outer cone is the cone outside which you cannot see any of the source.
{ See the attached image }

The region between these two cones (umbra) is where varying parts of the source are obscured and the brightness of the light will drop off to zero at the edge of the outer cone.

You get a reverse effect when you look at a shadow of say a circular object projected by a non-point light source. The edges of the shadow (umbra) will be fuzzy. This is the region between these two cones. You can treat the shadow as equivalent to the previous case where you allow the angles of the cones to exceed 180deg.In the case of say an actual flashlight with a reflector (widening the source and bringing it forward) the outer cone is actually the entire half-plane in front of the circular opening. You'll note that in looking at the front of a flashlight at any forward angle you see light. The reflector also projects a (usually out of focus) image of the source so the intensity is not uniform. If you want to test this, place some wax paper over the front of a flashlight to provide a uniform source and place the flashlight inside a box (painted black on the inside for best effect) with a circular opening.

 

[yuiop]

Hmmmmm... Anyone care to carry out a dual slit experiment with 2 separate light sources (possibly 2 tuneable lasers) and see if they can get any interferance patterns?

The idea is to see if an interferance pattern can be obtain without individual photons interfering with themselves, perhaps by putting a partition between the two light sources and the two slits on the source side of the slit barrier.

?

 

[jambaugh]

Hmmmmm... Anyone care to carry out a dual slit experiment with 2 separate light sources (possibly 2 tuneable lasers) and see if they can get any interferance patterns?

The idea is to see if an interferance pattern can be obtain without individual photons interfering with themselves, perhaps by putting a partition between the two light sources and the two slits on the source side of the slit barrier.

?

No matter how finely you tune the two lasers their frequencies it will be very very hard to match them up enough to produce a stationary interference pattern.

Here's one possibility: Take a non-linear crystal producing an EPR photon pair so their frequencies are exactly the same. Then use a pair of lasers acting in amplifier mode (rather than as oscillators) and amplify each photon of the pair into a coherent beam. You get two beams which should have matching frequencies.

But I say the experiment is not wholly necessary. The correspondence principle says beams with large numbers of photons will in the classical limit behave the same as classical e-m waves. In classical E-M the field is one entity "interfering with itself" regardless of how you chop its amplitude up into component quanta. Again "photons" are not objective particles, they are quanta and as such making distinctions about which interfered with which is meaningless.

In the example I gave you can still view the composite system as consisting of individual photons each in a superposition of originating in either of the two lasers, and in such a factorization "each photon is only interfering with itself". In the alternative factorization you chop photons up into left device and right device photons and all the interference is "between distinct photons".

It's all relative and so you can't make an absolute distinction.

 

[rcgldr]

Getting back to the OP, air will "difuse" (refract) light. There's also going to be some refraction at the edges of the cone. However your post seems to be about a rendering program, and I'm not sure of the goal of the rendering program. Some rendering programs are designed to give "atmosphere", so that air scatters the light, with a range from clear air to very foggy air.

Regarding the "dual lasers" why not use prisms to split a beam from a single laser then remerge the beams? This could be used to create a phase shift.

 

[jambaugh]

Getting back to the OP, air will "difuse" (refract) light. There's also going to be some refraction at the edges of the cone. However your post seems to be about a rendering program, and I'm not sure of the goal of the rendering program. Some rendering programs are designed to give "atmosphere", so that air scatters the light, with a range from clear air to very foggy air.

Regarding the "dual lasers" why not use prisms to split a beam from a single laser then remerge the beams? This could be used to create a phase shift.

The why of "dual lasers" was to be able to better say "distinct photons" are interfering instead of "photons which travel both paths of the beam splitter interfere with themselves". It is really a moot point and as you hint a digression from the OP.

 

[yuiop]

The why of "dual lasers" was to be able to better say "distinct photons" are interfering instead of "photons which travel both paths of the beam splitter interfere with themselves". It is really a moot point and as you hint a digression from the OP.

yes... a single laser and beam splitter brings the possibility of entangled photons into the picture which is another headache.


Back on the OP a combination of all the factors mentioned in the above posts, (flashlight design, reflection off dust particles, the umbra effect assoiated with diffraction from edges and scattering of light from object illuminated by the cone) all conspire to make a perfect light cone very unlikely. Any 3D light rendering program trying to create a realistic effect would not create a perfect light cone without any illumination outside the light cone.

 

[jambaugh]

...
Back on the OP a combination of all the factors mentioned in the above posts, (flashlight design, reflection off dust particles, the umbra effect assoiated with diffraction from edges and scattering of light from object illuminated by the cone) all conspire to make a perfect light cone very unlikely. Any 3D light rendering program trying to create a realistic effect would not create a perfect light cone without any illumination outside the light cone.

I don't think it's that difficult. As I say the umbra is not due to diffraction from edges but rather the width of the source vs the aperture. It can all be handled via ray tracing methods to give realistic effects. People keep bringing up diffraction here when the wavelength of visible light is so short vs aperture size that diffraction is not significant.