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Quote from: Bored chemist on 10/05/2022 18:20:40If 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? Quote from: hamdani yusuf on 10/05/2022 14:21:57Say W= 0.1 mm, while R=10 m
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.
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)
Quote from: Bored chemist on 11/05/2022 13:31:27You 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.
My assumptions are consistent with my assumptions and unaffected by your errors.
The "beam" will be about the same size as the sphere by the 10th reflection(Because 3^10 is 59049)
In my calculation
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.
mirror ball.jpg (37.2 kB . 615x618 - viewed 3108 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 beamIf 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?
Quote from: hamdani yusuf on 13/05/2022 14:39:35What 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.
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.
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.
The mirror at G is concave, which reduces the divergence.
Quote from: hamdani yusuf on 13/05/2022 16:48:52The 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.
Quote from: hamdani yusuf on 13/05/2022 16:48:52"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?
Quote from: Bored chemist on 13/05/2022 18:01:51Quote from: hamdani yusuf on 13/05/2022 16:48:52"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.
Why do you call it diffraction?
How much is the divergence caused by diffraction,
Quote from: hamdani yusuf on 19/05/2022 12:44:21Why do you call it diffraction?It was called diffraction before I was born.Quote from: hamdani yusuf on 19/05/2022 12:44:21How much is the divergence caused by diffraction, It depends.
This article shows the difference between Reflection,-Refraction,-and-Diffraction.