[Bored chemist]

If you shine a beam of light at a concave mirror it is brought to a focus.
The focal length is half the radius of curvature.
So the distance from the focal point (F) to the point (P) where the light strikes the mirror is half the radius of the sphere and, the distance to the other side of the sphere (G) is 3 times as big. (It's 3/4 times the diameter as opposed to 1/4 times the diameter)
That means the edges of the light form (roughly) two similar triangles , one 3 times as big as the other .
So the width of the beam when it strikes G is about 3 times W.

Now that (divergent) light beam is bounced back across the mirror.
If it was a parallel beam then the same thing would happen to it as happened to the original beam. It would be 3 times as big when it hit the mirror for a third time.
So it would be 9 times W.
But it was already diverging after the first reflection, so the width will be even bigger.

But to a rough approximation, the width of the beam, after n reflections is (at least) 3^n times bigger than the original beam.

What would I get in this case?

Say W= 0.1 mm, while R=10 m

You need my help to multiply 0.1 by 3?


The "beam" will be about the same size as the sphere by the 10th reflection
(Because 3^10 is 59049)

[hamdani yusuf (OP)]

You need my help to multiply 0.1 by 3?


The "beam" will be about the same size as the sphere by the 10th reflection
(Because 3^10 is 59049)

I want to make sure that your approximation still makes sense under your own assumptions, and it's not contaminated with my assumptions.

[Bored chemist]

My assumptions are consistent with my assumptions and unaffected by your errors.

[hamdani yusuf (OP)]

You need my help to multiply 0.1 by 3?


The "beam" will be about the same size as the sphere by the 10th reflection
(Because 3^10 is 59049)

You can calculate a complex equation and come out with correct value. But it doesn't necessarily represent the system in question.

[Bored chemist]

You need my help to multiply 0.1 by 3?


The "beam" will be about the same size as the sphere by the 10th reflection
(Because 3^10 is 59049)

You can calculate a complex equation and come out with correct value. But it doesn't necessarily represent the system in question.

Did you notice my use of the word "about"?

Also, do you really think that 3*3*3*3*3*3*3*3*3*3 is "a complex equation"?

[hamdani yusuf (OP)]

My assumptions are consistent with my assumptions and unaffected by your errors.

If you assume that your assumptions are already correct, you become blind to see your own errors. That's what happened to most religions and pseudoscience cults.

[hamdani yusuf (OP)]

The "beam" will be about the same size as the sphere by the 10th reflection
(Because 3^10 is 59049)

In my calculation, the width of the beam increases linearly to the number of reflection, instead of exponentially like in your approximation.

[Bored chemist]

In my calculation

I showed why it is exponential (actually, why it's faster than that).
You just made a claim with no supporting working.
You just assumed your assumptions were correct.

If you assume that your assumptions are already correct, you become blind to see your own errors. That's what happened to most religions and pseudoscience cults.

It's also often what I find has happened to people who are arguing with me on the internet.
Did you not realise you were doing exactly the same thing you accused me of?

[hamdani yusuf (OP)]

mirror ball.jpg (37.2 kB . 615x618 - viewed 961 times)Here's a very bad sketch, but it illustrates the point.
I drew the incoming beam. The thin lines represent the outside edges of the outgoing beam

If you shine a beam of light at a concave mirror it is brought to a focus.
The focal length is half the radius of curvature.
So the distance from the focal point (F) to the point (P) where the light strikes the mirror is half the radius of the sphere and, the distance to the other side of the sphere (G) is 3 times as big. (It's 3/4 times the diameter as opposed to 1/4 times the diameter)
That means the edges of the light form (roughly) two similar triangles , one 3 times as big as the other .
So the width of the beam when it strikes G is about 3 times W.

Now that (divergent) light beam is bounced back across the mirror.
If it was a parallel beam then the same thing would happen to it as happened to the original beam. It would be 3 times as big when it hit the mirror for a third time.
So it would be 9 times W.
But it was already diverging after the first reflection, so the width will be even bigger.

But to a rough approximation, the width of the beam, after n reflections is (at least) 3^n times bigger than the original beam.

This is essentially why integrating spheres work.

What is the width of the beam after it's reflected at G?

[Bored chemist]

What is the width of the beam after it's reflected at G?

Immediately after it is reflected (before it has gone back across the sphere) its width is still about 3W.
But it's strongly divergent. Even if the mirror at G was flat, it would reach about 3 or 4 W by the time it reached the opposite side of the sphere.

But the real question here is why do you have to ask me?

If you can't work it out for yourself, go and learn science.

[hamdani yusuf (OP)]

What is the width of the beam after it's reflected at G?

Immediately after it is reflected (before it has gone back across the sphere) its width is still about 3W.
But it's strongly divergent. Even if the mirror at G was flat, it would reach about 3 or 4 W by the time it reached the opposite side of the sphere.

But the real question here is why do you have to ask me?

If you can't work it out for yourself, go and learn science.

Does it increase exponentially by the number of reflection?
The mirror at G is concave, which reduces the divergence.
Because you're the one who said

Diffraction stops it being scientific.

But to a rough approximation, the width of the beam, after n reflections is (at least) 3^n times bigger than the original beam.

While I suggested to consider only the center of the beam.

It depends on the width of the light beam and the curvature of the mirror. But you can restrict the calculations for the center of the light beam.

"When an honest man discovers he is mistaken, he will either cease being mistaken, or cease being honest." - Anonymous.

[Bored chemist]

The mirror at G is concave, which reduces the divergence.

No.
A parallel beam striking a concave mirror is brought to a focus, but after that the beam diverges strongly.

I see you still haven't actually drawn what happens.

[Bored chemist]

So, did you change the thread title to " How many times would THE CENTRE EDGE OF a light ray be reflected inside a circular mirror?" or did you cease being honest about it?

[hamdani yusuf (OP)]

The mirror at G is concave, which reduces the divergence.

No.
A parallel beam striking a concave mirror is brought to a focus, but after that the beam diverges strongly.

I see you still haven't actually drawn what happens.

It's reduced compared to flat mirror. That's why I said that the width increases linearly to the number of reflection, instead of exponentially.

[hamdani yusuf (OP)]

"When an honest man discovers he is mistaken, he will either cease being mistaken, or cease being honest." - Anonymous.

So, did you change the thread title to " How many times would THE CENTRE OF a light ray be reflected inside a circular mirror?" or did you cease being honest about it?

It also applies to the edge of a light ray.

[Bored chemist]

"When an honest man discovers he is mistaken, he will either cease being mistaken, or cease being honest." - Anonymous.

So, did you change the thread title to " How many times would THE CENTRE OF a light ray be reflected inside a circular mirror?" or did you cease being honest about it?

It also applies to the edge of a light ray.

All light beams are (eventually) divergent- because of diffraction.
So, if the centre of a beam enters the circular mirror at 10 degrees, the edge of it doesn't.
And that means your puzzle is poorly defined.

[hamdani yusuf (OP)]

All light beams are (eventually) divergent- because of diffraction.

Why do you call it diffraction?
How much is the divergence caused by diffraction, compared to the curvature of the mirror?

[Bored chemist]

Why do you call it diffraction?

It was called diffraction before I was born.

How much is the divergence caused by diffraction,

It depends.

[hamdani yusuf (OP)]

Why do you call it diffraction?

It was called diffraction before I was born.

How much is the divergence caused by diffraction,

It depends.

This article shows the difference between Reflection,-Refraction,-and-Diffraction.
https://www.physicsclassroom.com/class/waves/Lesson-3/Reflection,-Refraction,-and-Diffraction





And in this article, no mention of diffraction is found.
Reflection and the Ray Model of Light - Lesson 3 - Concave Mirrors
The Anatomy of a Curved Mirror
https://www.physicsclassroom.com/Class/refln/u13l3a.cfm

[Bored chemist]

This article shows the difference between Reflection,-Refraction,-and-Diffraction.

Why did you post it?