Why does the angle of incidence = the angle of reflection?
A lot of physics books explain that when a light ray strikes a reflective surface, it will reflect at an angle equal to the angle it strikes the surface. That is, the angle of incidence equals the angle of reflection. This physical phenomenon seems reasonable enough, but just why are the two angles equal?
As we know from trigonometry, angles have horizontal and vertical components, and so do vectors which are useful for the study of moving things that have direction. Since a ray of light moves in a particular direction, its angle of direction or vector can be described using horizontal and vertical components.
Consider a ray of light that is oblique to a reflective surface. Say it is moving from left to right from the point of view of an observer. After this ray strikes the surface and bounces off the surface, it will maintain its horizontal component of motion because very little energy is absorbed by the reflective surface, and energy conservation dictates that the light energy must be maintained. This same conservation law dictates that the energy of the light ray must stay the same in the vertical direction as well. However, unlike the horizontal component of the light-ray vector, the vertical component is reflected off the surface in the opposite direction at which it struck the surface. That is, instead of striking directly downward on the surface, it now moves directly upward from the surface.
Comparing the incident light ray with the reflected light ray, the aforementioned observer sees that the two rays are virtually identical in energy and in their horizontal components, but the equal and opposite vertical components result in the direction of the two rays forming equal angles to a line that is perpendicular to the reflective surface.
Is my reasoning correct?
Jagella
Re: Why does the angle of incidence = the angle of reflectio
Quote:
Originally Posted by Jagella
A lot of physics books explain that when a light ray strikes a reflective surface, it will reflect at an angle equal to the angle it strikes the surface. That is, the angle of incidence equals the angle of reflection. This physical phenomenon seems reasonable enough, but just why are the two angles equal?
http://en.wikipedia.org/wiki/Fermat's_principle
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Originally Posted by Jagella
As we know from trigonometry, angles have horizontal and vertical components,
No, they don't. This statement is absurd.
Quote:
Originally Posted by Jagella
and so do vectors which are useful for the study of moving things that have direction. Since a ray of light moves in a particular direction, its angle of direction or vector can be described using horizontal and vertical components.
You can resolve the vector associated with the direction of a light ray into convenient components, but you cannot reslve an angle into "components". However it is enough, in knowledgeable hands (which excludes you) to resolve the vector.
Quote:
Originally Posted by Jagella
Consider a ray of light that is oblique to a reflective surface. Say it is moving from left to right from the point of view of an observer. After this ray strikes the surface and bounces off the surface, it will maintain its horizontal component of motion because very little energy is absorbed by the reflective surface, and energy conservation dictates that the light energy must be maintained.
You seem to be somehow equating the energy of a photon with kinetic energy of some massive particle. Moreover you appear to be treating energy, a scalar, as though it were a vector. This is just wrong.
In a pure reflection, energy is conserved, but not for the reasons that you appear to be assuming (your logic is so fuzzy it is a bit hard to tell what you are thinking, and errors abound).
In any case the logic here is badly flawed.
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Originally Posted by Jagella
This same conservation law dictates that the energy of the light ray must stay the same in the vertical direction as well.
Completely wrong as now it is clear that you are treating energy as a vector. It is not.
Quote:
Originally Posted by Jagella
However, unlike the horizontal component of the light-ray vector, the vertical component is reflected off the surface in the opposite direction at which it struck the surface. That is, instead of striking directly downward on the surface, it now moves directly upward from the surface.
This is inane. It is basically just a garbled restatement of what is meant by "reflection", but devoid of physics. There are only two possibilities for the "vertical component" of motion -- away from the mirror or into it. Reflection is generally taken as choosing the path to be away from the mirror. If you go through the looking glass be on the lookout for a young girl and a rabbit with a watch.
Quote:
Originally Posted by Jagella
Comparing the incident light ray with the reflected light ray, the aforementioned observer sees that the two rays are virtually identical in energy and in their horizontal components, but the equal and opposite vertical components result in the direction of the two rays forming equal angles to a line that is perpendicular to the reflective surface.
Is my reasoning correct?
Jagella
No. There is no logic whatever in evidence. You simply took the known answer (angle of incidence= angle of reflection), made a bunch of incorrect and/or inane observations and regurgitated the known answer.
You desperately need a re-education (more likely education for the first time) in high school mathematics and elementary physics. I shudder to think that you actually offer instruction to innocent young folks.
Re: Why does the angle of incidence = the angle of reflectio
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Originally Posted by DrRocket
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Originally Posted by Jagella
As we know from trigonometry, angles have horizontal and vertical components,
No, they don't. This statement is absurd.
Quote:
Originally Posted by Jagella
and so do vectors which are useful for the study of moving things that have direction. Since a ray of light moves in a particular direction, its angle of direction or vector can be described using horizontal and vertical components.
You can resolve the vector associated with the direction of a light ray into convenient components, but you cannot reslve an angle into "components". However it is enough, in knowledgeable hands (which excludes you) to resolve the vector.
I'm sure the wrong words were used. However, taking Tan(Theta) of any angle will yield the angle's equivalent rise/run relationship. If a person wants to call that vertical/horizontal, that wouldn't be un-descriptive.
I think the need to use a particular wording/jargon is why I've never really enjoyed the formalization of mathematical problems. It feels too much like I'm in an English class instead of a math class.
Quote:
Quote:
Originally Posted by Jagella
Consider a ray of light that is oblique to a reflective surface. Say it is moving from left to right from the point of view of an observer. After this ray strikes the surface and bounces off the surface, it will maintain its horizontal component of motion because very little energy is absorbed by the reflective surface, and energy conservation dictates that the light energy must be maintained.
You seem to be somehow equating the energy of a photon with kinetic energy of some massive particle. Moreover you appear to be treating energy, a scalar, as though it were a vector. This is just wrong.
In a pure reflection, energy is conserved, but not for the reasons that you appear to be assuming (your logic is so fuzzy it is a bit hard to tell what you are thinking, and errors abound).
In any case the logic here is badly flawed.
Yeah. Quite so.
Jagella, if you want to understand how light works, you're going to have to be prepared to take most of your notions of how objects move/interact, and allow them to be turned sideways, upside down, and inside out, because light doesn't always move or interact in a way that would be intuitive from everyday experience.
Re: Why does the angle of incidence = the angle of reflectio
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Originally Posted by kojax
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Originally Posted by DrRocket
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Originally Posted by Jagella
As we know from trigonometry, angles have horizontal and vertical components,
No, they don't. This statement is absurd.
Quote:
Originally Posted by Jagella
and so do vectors which are useful for the study of moving things that have direction. Since a ray of light moves in a particular direction, its angle of direction or vector can be described using horizontal and vertical components.
You can resolve the vector associated with the direction of a light ray into convenient components, but you cannot reslve an angle into "components". However it is enough, in knowledgeable hands (which excludes you) to resolve the vector.
I'm sure the wrong words were used. However, taking Tan(Theta) of any angle will yield the angle's equivalent rise/run relationship. If a person wants to call that vertical/horizontal, that wouldn't be un-descriptive.
I think the need to use a particular wording/jargon is why I've never really enjoyed the formalization of mathematical problems. It feels too much like I'm in an English class instead of a math class.
1. Note my comment (here in bold), which reflects what one really wants to do.
2. The proper formulation, which is a lot more than semantics, is important. Remember, this nut ball claims to be giving instruction to young people on the subject of mathematics -- shudder.
