Light propagation orthagonal to vector - math help needed.

[quantum quack]

Hi peoples,

A little math question that should be relatively easy for you but difficult for a math illiterate such as myself.

I was going to draw some fancy diagrams but decided to pose my question verbally to begin with and if need be draw the diagrams later.

It is all about how light propagates as a spherical wave form from it'ss source and how that sphere of light waves impacts on a flat surface orthagonal to the vector of that wave.

OK, by way of explaining we have a sphere resting on a flat surface. The point of contact theoretically is an impossibly small point , assuming a perfect sphere and perfect surfaces of sphere and flat surface.

Now if we imagine the sphere penetrating the flat surface and we take a cross section of the sphere. The diameter of that cross section expands as the sphere penetrates.

The question is:

What is the relationship mathematically to the growth of the cross section to the velocity of the spheres penetration?

If we assume our sphere is a photonic wave hitting a flat surface it seems obvious that the reflected light on our surface rather rapidly expands as the photonic wave passes.

I would initially surmise that the orthagonal expansion would start from 'c' and reduce it's expansion rate immediately. In other words the reflection expansion rate is never at 'c' but always slowing from 'c', due to the nature of a sphere's impact point being impossible theoretically to measure.
But once contact has been made by our photonic wave the rate of expansion must start to slow from 'c'.

Do I need to draw some diagrams?

Am I correct in my assessment that reflection propogation across the surface is never 'c'?

What is the mathematical relationship to the velocity of the photonic sphere and the reflections propagation across the reflective surface?

Is there a better way of expressing the question?

The thinking:
When measuring the speed of light are we measuring the leading point of the photonic wave or are we measuring later aspects of the wave? How does the energy from the wave propagate through absorbtion within our flat surface?
When measuring the velocity of light could we be measuing the reflections propagation rate and not the velocity of the photonic wave itself?
Could the time lag in waves impact across the flat surface be some how fundamental to what energy is regarding space and time.

any help or discussion would be appreciated

[quantum quack]

I just realised that I had it arse about.....the propagation rate must be in excess of 'c' and reducing. [possibly intantaneous reducing as the wave penetrates]

[maddog]

Originally Posted by quantum quack

What is the relationship mathematically to the growth of the cross section to the velocity of the spheres penetration?

If we assume our sphere is a photonic wave hitting a flat surface it seems obvious that the reflected light on our surface rather rapidly expands as the photonic wave passes.

I would initially surmise that the orthagonal expansion would start from 'c' and reduce it's expansion rate immediately. In other words the reflection expansion rate is never at 'c' but always slowing from 'c', due to the nature of a sphere's impact point being impossible theoretically to measure.
But once contact has been made by our photonic wave the rate of expansion must start to slow from 'c'.

The thinking:
When measuring the speed of light are we measuring the leading point of the photonic wave or are we measuring later aspects of the wave? How does the energy from the wave propagate through absorbtion within our flat surface?
When measuring the velocity of light could we be measuing the reflections propagation rate and not the velocity of the photonic wave itself?
Could the time lag in waves impact across the flat surface be some how fundamental to what energy is regarding space and time.

When I first read this, I created the visual of a sphere with a plane slicing the sphere. The size of the
circle on the plane (that touches the sphere) is dependent on what percentage of the radius of the
sphere that is incident with the plane and normal to it. I never was able to create where 'c' was.
Note: from a point source light expands radially in all directions from that source. Whereas
photons are packetized light waves. This means their relative size is typically on the order
of yet can be significantly less than the wavelength of that light. Reflected light travels at
the same speed of light in the same medium. Each photon goes in a specific direction and has a certain
energy (wavelength/frequency) and goes until it gets absorbed. The dual nature of light allows
anothe rmethod to describe the light as a wave whereby the sum total of light can be integrated
around the sphere in a contious fashion. Does this help.

maddog

[quantum quack]

Maddog thanks for your reply.
It helps a little but unfortunately it looks like I am going to have to submit some simple diagrams to expose my question properly. I'll post them tomorrow.....

[Qfwfq]

Originally Posted by quantum quack

.....the propagation rate must be in excess of 'c' and reducing. [possibly intantaneous reducing as the wave penetrates]

Quite right, the locus of points having a given phase is a circumference of increasing radius r, equal to the sine of an angle given by the ratio of distance to the surface over radius of the sphere. You can work it out for a circle and a line, in 2-D.

[quantum quack]

Maddog, as a matter oif interest I was considering the notion that our photon could actually be the entire wave. In other words the radius of our photon would be 299792kms after 1 second from emmission.[expanding outwards in a vacuum - "photon shell"]....

who says that a photon has to be small.....ha

[quantum quack]

Ok I did these two diagrams as a way of clarifying my question.
The first one is an animation:





My interest is in the relationship between the radius, the speed of radius increase [which is always 'c'] and the speed of growth in the reflection.

From what I see there would be two curves involved, the curve of the wave and the plotted curve of the reflections growth.

I was interested in how they would compare and how the radius effected those two curves.

I do believe Q has given the formula for which I thank him/her for.....

Maybe Q or someone else can help me in working out how to ask this question properly?

it seems to me that the ratios involved will change as the distance betweeen light source and reflector changes. Noting that this is different to just an increace in radius due to light propagation.

Ie:

Distance to star is 4 light years, wave propagation is 'c', the reflector is stationary relative to Light source, compared to :
Distance to light bulb in room is 10 meters, wave propagationis 'c', walls are stationary to source.

The curves involved are would be very differnet me thinks....so the relationship with distance between source and reflector is very important.

Please excuse my rambling......just trying to work through this light, distance curve relationship.......

[quantum quack]

Another diagram to show my quest: