[hamdani yusuf (OP)]

How many times would a light ray be reflected inside a circular mirror?

Let's say we have a circular mirror which is reflective in inner side. A laser beam is shone through a small hole on the mirror. How many times the laser beam would be reflected, if the incoming angle is 10 degrees?

[chris]

This is effectively how a fibre optic works.

[hamdani yusuf (OP)]

This is effectively how a fibre optic works.

I think the answer for the question needs math technique/tricks which are not readily available in most school textbooks.
There are more to explore, which I'll add to the playlist later as I have the time.

Sorry for the wrong link I put in the opening post. It has been corrected now.

[chris]

I think the answer will depend upon the quality of the mirror; even tiny losses will quickly turn all of the energy in the photons into heat.

[guest39538]

How many times would a light ray be reflected inside a circular mirror?

Let's say we have a circular mirror which is reflective in inner side. A laser beam is shone through a small hole on the mirror. How many times the laser beam would be reflected, if the incoming angle is 10 degrees?

There is no angle using a circle, the light remains linear.

[hamdani yusuf (OP)]

I think the answer will depend upon the quality of the mirror; even tiny losses will quickly turn all of the energy in the photons into heat.

Let's assume that the loss from the mirror is negligible, at least until the light exit again through incoming hole.

First step to answer the question about reflection of light in a circle. Introducing a new variable : order of reflection. Using incoming angle to calculate ratio between order of reflection and number of reflection.

[hamdani yusuf (OP)]

Next step to answer the question. Discovering a hidden variable implicitly stated in the question, which is greatest common factor between order of reflection and number of reflection.
After the value of s is obtained, we need to subtract by 1 to get the number of reflection, because when the head of the ray comes back to incoming point, it will leave the circle.

[Bored chemist]

If the beam has a finite width (and diffraction means it will have) them you need to consider the "focussing" effect of the curved mirror.
Essentially the light will be scattered in every direction.
Incidentally, unless the mirror has infinite mass, the wavelength will also be scrambled.

[hamdani yusuf (OP)]

I see this as an idealized math problem instead of realistic physics problem.
The effects from finite width of the light beam can be addressed/minimized by making the circle large enough.

[Bored chemist]

So, not actual science then...

[hamdani yusuf (OP)]

So, not actual science then...

It's a math problem. If you don't think that math is science, then you're right.

[Bored chemist]

So, not actual science then...

It's a math problem. If you don't think that math is science, then you're right.

It would be a math problem if the mirror was a polygon.

[hamdani yusuf (OP)]

It would be a math problem if the mirror was a polygon.

Why does it stop being math problem when the number of sides of the polygon is increased toward infinity, i. e. becomes a  circle?

[Bored chemist]

It would be a math problem if the mirror was a polygon.

Why does it stop being math problem when the number of sides of the polygon is increased toward infinity, i. e. becomes a  circle?

Because it stops working.
If a beam of light hits a curved surface, it's no longer a beam.

[hamdani yusuf (OP)]

Because it stops working.
If a beam of light hits a curved surface, it's no longer a beam.

What prevents a mathematical ray from having infinitesimally narrow width? 

[Bored chemist]

Diffraction stops it being scientific.

[hamdani yusuf (OP)]

In geometry, a ray can be defined as a part of a line that has a fixed starting point but no end point.

[Bored chemist]

How many times would a light geometric ray be reflected inside a circular mirror?

[hamdani yusuf (OP)]

Diffraction stops it being scientific.

How does a curved surface create diffraction?

[Bored chemist]

Diffraction stops it being scientific.

How does a curved surface create diffraction?

I wasn't aware that anyone had said that it did.