How many times does the light reflect?

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In summary, the conversation discusses the possibility of finding a general equation for the number of times a light beam is reflected by the legs of an isosceles triangle and the height of the beam based on the angle and number of reflections. The question also asks if there is a proof for all beams eventually coming down to the base. The conversation also mentions a special case where the beam is reflected back to the same corner. The solution involves setting up an equation based on the equal incoming and outgoing angles at each reflection.
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Papatom
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My question is inspired by this thread:
https://www.physicsforums.com/threads/can-you-solve-this-geometry-problem-for-nine-year-olds.890794/

If you an isosceles triangle and you put in a corner (or somewhere else) a light beam (laser) the beam will reflect one or more times before it comes down to the base. See picture. Is there a general equation for how many times the light is reflected by the legs? Can you calculate from the angle and how many reflections there are how high the beam comes. It is evident that all beams must come down to the base again. Is there a proof for?

Triangle number 1 is the 9-years old question. If the angle of the laser with the base gets larger, the beam gets more and more reflected until it is reflected downwards again. Points A and C are the special cases were the beam is reflected back to the same corner.

Does anyone knows if there math available to calculate this?
 

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At every reflection, the incoming angle (relative to the surface) is equal to the outgoing angle. That allows to set up a short equation how the angle (relative to the base, for example) changes with every reflection. Based on that it is possible to find a general formula.
 

1. How is the number of light reflections determined?

The number of light reflections is determined by the number of reflective surfaces that the light encounters. Each time the light hits a reflective surface, it will bounce off and create a new reflection.

2. Does the type of surface affect the number of light reflections?

Yes, the type of surface does affect the number of light reflections. Smooth and polished surfaces, such as mirrors, will create more reflections compared to rough and matte surfaces.

3. Can the number of light reflections be calculated?

Yes, the number of light reflections can be calculated using the formula n = 2^(n-1), where n is the number of reflective surfaces. For example, if there are 3 reflective surfaces, the light will reflect 2^(3-1) = 4 times.

4. Does distance affect the number of light reflections?

No, the distance does not affect the number of light reflections. As long as the light encounters reflective surfaces, it will continue to reflect regardless of the distance between them.

5. Can the number of light reflections be infinite?

Theoretically, the number of light reflections can be infinite if the light continues to encounter reflective surfaces. However, in practical situations, the intensity of light decreases after each reflection and eventually becomes too weak to be perceived by the human eye.

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