All these are related I believe: What is the physical process by which
a mirror reflects a photon? Why are ~5% of photons not reflected
(assuming a very high quality first surface mirror?) Why is the photon
reflected at the angle of incidence? Are any properties of the photon
changed by reflection? Is there any limit to the number of photons
that a mirror can reflect simultaneously (assuming multiple light
sources illuminating a mirror from all possible angles?) What
experiment (documented) has proven the answer to these questions?

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Request for Question Clarification by hedgie-ga on 24 Aug 2006 10:38 PDT

All question can be answered, but I am a bit at loss about this requirement

 "What experiment (documented) has proven the answer .."
Hi 

What does documented mean?  Law of refraction is known from the times of
Newton. Today physicists do not write papers about that - but it is performed
often in the classrooms. 

 So, is something like this considered as 'documentation'? 

http://www.physics.umd.edu/courses/Phys375/RolstonFall05/lab1.pdf#search=%22reflection%20of%20light%2C%20experiment%22

Also,  "What is the physical process.."  Is answer 'process is called
reflection' a sufficient answer?

---

Clarification of Question by billa999-ga on 24 Aug 2006 11:16 PDT

"Process" means what actual interaction between the photon and some
physical aspect of the mirror. At some point on the path to the mirror
the photon encountered something that "reflected" it. What happened,
what physical process caused the photon to go of in a different and
very specific direction?

"Documentation" would be the paper or papers that explained the
physical process of reflection.

Photon has zero REST mass, but it has a momentum. 
  Magnitude of this vector is E/c = h *ñ /c
  where ñ stands for Greek letter ni meaning frequency,
  direction is direction of travel.
  When photon hits a conductive surface (interface between glass and
silver coating)
  the two components of this vector behave differently: 
  normal component (perpendicular to the mirror surface) changes signs
  tangential component (parallel to the mirror surface) is unchanged

  Result is reflection according to the Snell law:
http://acept.asu.edu/PiN/rdg/reflection/reflection.shtml


Here is a video of actual experiment
  On a flat mirror, the angle of incidence is equal to the angle of reflection.
http://www.wfu.edu/physics/demolabs/demos/avimov/bychptr/chptr9_optics.htm

  This mechanism is same as when reflection of a ball from a rigid surface:

  http://www.lhup.edu/~DSIMANEK/ideas/bounce.htm

   During the reflection  (bounce) the momentum is transfered to the
mirror (massive wall)
   that give rise to radiation pressure
 http://www.u.arizona.edu/~lilley98/

 That is simple case. Things can get more complex when we consider real;
 materials (which are not perfectly conductive or rigid) and spin:

http://www.physics.usyd.edu.au/~cross/Gripslip.pdf.
 
   Photon also has an angular momentum or spin, which is manifested as
polarization of light.
   As you probably know, light (as other elementary particles) has
particle and wave properties,
   and for some phenomena (photo-effect) the description by particle
model is more suitable,
   for other (reflection is one example) the wave model is more
suitable. For some effects, the
   complex math of QED is required.

simple expose of QED
http://en.wikipedia.org/wiki/Quantum_electrodynamics
more complex
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/qed.html
popular books
http://www.amazon.com/gp/richpub/listmania/fullview/1SYJYH1NOKUW0/102-6271296-4091321?%5Fencoding=UTF8

For most phenomena of reflection, QED would be an overkill. When the
thickness of the optical layers
is comparable to the wavelength of the light, such as in
antirefelction coatings of lenses
http://en.wikipedia.org/wiki/Optical_coating
very complex phenomena can be adequately described by (simple, matrix)
calculus based on the wave
picture of light. (note the picture of lambda/4 reflection in the above article).

That (thin film theory) is important engineering discipline based on
Maxwell equations
https://www.omegafilters.com/index.php?page=tech_fildes_tft    (see
technical articles)
which also describes non-perfect materials, which absorb certain
proportion of light
(in case of ordinary mirror at room temperature - about 5% photons get
absorbed instead of reflected,
in case of 'semi-transparent' (half-slivered) mirror, some get refracted.
http://www.williamson-labs.com/optical-body.htm

Let's se if I covered all of your sub-questions:

3) Are any properties of the photon changed by reflection?

 Yes. Momentum, and sometimes spin.
4) Is there any limit to the number of photons
 Well, not really, in general. However, if you shine too much light
 on the mirror - it will heat up (by absorbed photons) and that may change its
 properties. More complex is entanglement: Normally photons do not interact which
 each other (there are bosons, not fermions) -- Maxwell Equations are linear.
But, if photons come from same coherent source (a laser beam, split in two, and
brought together again, there could be interference).  See

SEARCH TERM : interference of photons

It can get quite complex and in some cases QED has to be invoked.
Here are few technical articles on this

http://www.citebase.org/abstract?id=oai%3AarXiv.org%3Aquant-ph%2F0208174

------------------------

Don't miss this paper from the Zeilinger group:

" R. Kaltenbaek et al, PRL 96, 240502 (2006).

In particular, read the first paragraph:

Is it possible to observe fully destructive interference of photons if
they all originate from separate, independent sources? Yes, according
to quantum theory. The perfect interference of photons emerging from
independent sources cannot be understood by the classical concept of
the superposition of electromagnetic fields but only by the
interference of probability amplitudes of multiparticle detection
events. As stressed by Mandel ??this prediction has no classical
analogue, and its confirmation would represent an interesting test of
the quantum theory of the electromagnetic field?? .."

---------------------
http://www.physicsforums.com/archive/index.php/t-124474.html

There is number of sites, of varied depth and complexity, which
illustrate these processes,
as  #42, #46, #48, #68 in this following list 

http://www.cordonline.net/laserapplets/

If something is not covered, please post an RFC. Else, rating is appreciated.

Hedgie

I understand that photons have mass, hence are influenced by gravity.

When a photon is reflected by a mirror, I wonder how much force is
exerted on the mirror due to the change in momentum of the photon ?

Hello sorwin,

   Photons have no mass. But they fall in gravitational fields
nonetheless. Remember the findings of Galileo: objects in a given
gravitational field fall with identical accelerations independent of
their masses.

   This result can be computed directly from Newtonian principles.

Newton's force law: F = ma (force is proportional to the product of
mass & its acceleration)

Newton's gravitational law: F = GMm/r^2 (force is proportional to the
gravitational constant, G, the masses of two interacting objects, M &
m, and inversely proportional to the square of their distance, r^2)

   So, GMm/r^2 = ma. Dividing both sides by m yields GM/r^2 = a.

   This is consistent with gravity as determined by general
relativity. In GR a region with momentum-energy content greater than
its surroundings will induce differentiation in the geometric
properties of space. External objects immersed in this distorted space
will accelerate according to the properties of space right there where
they are. Gravity is then due to local conditions, rather than to the
distant Earth, etc. In this theory it's absolutely required that
light, without mass, will fall in a gravity field just like any other
object.

   But even though the photon is massless, it still carries momentum,
p = h/lambda, with h = Planck's constant, and lambda = the wavelength.
So a light interactant material will be subject to the momentum of
light incident upon it.

billa999,

   I suggest you read Feynman's book, QED: The Strange Theory of Light & Matter. 

   Keep in mind that light reflection is a classical approximation.
For large numbers of photons (intense light), the angle of incidence
will tend to equal the angle of reflection.

   But on the atomic scale, a single photon will be absorbed by a
single orbital electron bound to a single atom, raising the electron
to a higher energy orbital. A very short time later the electron will
re-emit a new photon, surrendering energy and falling to a lower
orbital. The direction taken by the photon is entirely random; it
could scatter anywhere. But large numbers will interfere with one
another. Their frequency phases will superpose both destructively &
constructively. Depending upon the overall configuration of the
system, the sum total of all these interfering phases will average out
to the gross behavior of light with which we are familiar on the large
scale.

   But for more in-depth insight to this whole scheme of things, read the book.

It should be noted that, classically, the angle of incidence ought to
be expected to equal the angle of reflection, due to conservation of
momentum. Momentum-carrying light, incident upon a reflective surface,
has a component of motion parallel to the surface, and that component
has its own component of momentum. It's not surprising then that it's
observed (on the classical scale) to scatter off the surface at an
angle which carries that same magnitude of momentum.

   In fact, the classical conservation laws, including for energy, are
generally consequential to the quantum mechanical nature of
interactions.

I think mirrors do just fine one photon at a time. For example the
deep space Hubble image. Taken over many days were only seeing the
occasional photon but the image was most certainly formed.

Hi billa,

   Let's say that an astronomical object is so weak as its image
reaches Earth that not more than one photon interacts with the Hubble
mirror at any one instant. Quantum mechanically, each photon can
scatter in any specific direction at random. But not all directions
will have equal probability. There will be a spectrum of possible
scattering angles, with a narrow interval containing those with the
greatest likelihoods.

   A single photon may scatter in any direction. But for many
scatterings of many photons, the average scattering angle -the angle
of reflection- will tend toward the classical limit.

Hmm, that is something to consider. Suppose we did something like
this: Have a small half sphere with the inner surface coated with a
photo sensitive film. Place this on top of a first surface mirror. Put
a light source at the top of the sphere so photons, one at a time
would enter, hit the mirror, and be reflected directly back to the
source. Now some claim that some photons will be randomly reflected in
some other direction. These photons should hit the photosensitive
material. Assuming we continue the experiment until we get
quantifiable results when the photo sensitive film is developed, what
will the results be? A uniform number of the random photons hitting
all areas? More hitting near the light source? What will we see?

Hi again,

   This sort of experiment has been done. Not necessarily with the
exact apparatus you describe. But experiments have been done in which
low intensity light -one photon at a time- is allowed to generate an
image on a detector. The most common variant of this is diffraction of
light through either a tiny hole or thin slit.

   Intense light is, as one expects, diffracted, generating a
diffraction pattern on a detector (for example, a photographic film,
or a charge-coupled device). The pattern for the small hole is an
"Airy" pattern; concentric rings of alternating light & dark. For the
slit it's parallel bands of light & dark.

   In experiments such that the source is so weak as to emit only one
photon at a time, a photon may pass through the opening on its way to
the detector. The photon then registers at some location on the
detector. Let's say that we only expose the detector 'til exactly one
photon registers. Let's also say that we repeat this many times, one
photon each. We'll end up with a large number of images of single
photon exposures, distributed randomly. If we then superimpose all the
single images to display them in one, cumulative image, the
distribution becomes obvious: the single photons choose their paths
randomly, but the overall distribution for many will clearly be that
of the classical diffraction pattern.

   In fact, if you allow a detector to be exposed to an increasing
number of single photon events, it'll accumulate the same sort of
distribution. As the number of photon exposures increases, the
distribution tends toward the classical limit.

   Now I don't know off hand if the precise sort of arrangement you've
proposed has been done. But it has been done with diffraction as I've
described, and yours basically starts out with diffraction (at the
entry hole). So I'll say with confidence that your arrangement will
tend to generate a classical distribution in the same way.

". . . Interestingly, all Hubble images are created with
black-and-white cameras. Ones and zeros are sent to Earth. Color is
dropped in later with the popular Photoshop program.

http://www.space.com/scienceastronomy/astronomy/color_universe_020625-1.html

I'm not sure what the color separations in an astronomical photo have
to do with the original question, but whatever.

   When that article mentions that the colors are "dropped in later
with Photoshop", it doesn't mean that the colors are applied randomly
or arbitrarily. The image sensors on the Hubble telescope are
monochrome, but each image is photographed three separate times, each
through its own primary color filter. What the CCD then registers is a
field of intensities in a single elemental color. With three such
images, each filtered for one primary color, a faithful full color
image can be created.

   The data are downloaded to Earth, and the original color field
registered by each filtered image can be reproduced by simply
instructing the image editing software to color all pixels the color
which was admitted by the filter on the telescope. Three color
separations are produced in this way, which can then be composited to
make a full color image.

   This is basically the same thing that higher quality digital video
cameras do. They pass the image through a beam splitter, which then
distributes the original image to three separate CCDs, each
registering its own primary color. This maximizes the control which
can be exerted over the color balance in the video.

qed100 and billa999

Just a couple of corrections:  qed you almost got it, where you went
slightly wrong is the statement of "a single electron in an orbital
..." to paraphrase you.  Metals are characterized by overlapping
energy states in the outer orbitals which smear into bands because of
quantum mechanics.  Because of this a given electron is not associated
with a given atom, a more accurate model is that these electrons smear
out and form a conductive plane.  the electrons are confined by the
work function of the surface but are available to interact with
photons. If the photon has sufficent energy, it will liberate an
electron (einstein won a nobel for this work), if it doesn't the
energy is then kicked back out in the form of an photon.  Energy is
conserved.  Some energy is lost due to scattering and electron
interaction whilst it is excited.  This is more of a quantum
mechanical view.  A more classical view is that the metal has a
complex (as in using imaginary numbers) index of refraction which is
causes reflection.

As to mass and momentum and gravity... This is kinda hard to get ones
head around.  Photons are massless but have momentum, it is ultimately
tied up with why mass has energy.  But to keep on topic, photons are
strictly not affected by gravity.  However, gravity (through Einsteins
general theory of relativity) does affect and can warp spacetime,
which photons notice.  This is the effect of gravitational lensing
that you no doubt have heard about as a proof.

Good question billa999, a seemingly simple question can reveal some subtle aspects.

Hope this helps