# Thread: Why does the angle of incidence = the angle of reflection?

1. 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

2.

3. 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

Originally Posted by Jagella
As we know from trigonometry, angles have horizontal and vertical components,
No, they don't. This statement is absurd.

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.

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.

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.

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.

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.

4. Originally Posted by DrRocket

Originally Posted by Jagella
As we know from trigonometry, angles have horizontal and vertical components,
No, they don't. This statement is absurd.

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.

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.

5. Originally Posted by kojax
Originally Posted by DrRocket

Originally Posted by Jagella
As we know from trigonometry, angles have horizontal and vertical components,
No, they don't. This statement is absurd.

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.

6. What I've found tutoring people through lower level math is that the best way to get them to understand it is to let them figure out the concept first, even if they get the wording wrong. Just let them get the wording wrong.

Once they understand the concept, then afterwards you explain to them that they've been using the wrong words and tell them what the right words are.

If you teach them in that order, even people with very low scholastic IQ can understand mathematics. If you start with the wording, it's very easy for them to become confused and give up. Think about it: how can they assign meaning to a word that describes an object they don't even understand yet? It's easier to use concepts they already understand, and build on them.

7. @Jagella

I think you see the phenomenon clearly. By definition, a surface cannot alter rays traveling parallel to it, and it reflects rays perpendicular to it. Thus, a surface affects rays at angles between parallel and perpendicular according to their parallel and perpendicular components -- and the affects are additive.

8. Originally Posted by jrmonroe
@Jagella

I think you see the phenomenon clearly. By definition, a surface cannot alter rays traveling parallel to it, and it reflects rays perpendicular to it. Thus, a surface affects rays at angles between parallel and perpendicular according to their parallel and perpendicular components -- and the affects are additive.
Thanks a lot for an intelligent reply!

Please understand that when I described a light ray as a "vector," I didn't mean to say that it is a vector like a velocity or force vector. I meant that it has direction.

Isn't a reflected light ray similar to a rubber ball bouncing off of a floor? If I toss the ball directly down on the floor, it will bounce vertically. If I toss the ball along the floor, then it won't bounce at all but will just move parallel to the floor. If I toss it onto the floor at an acute angle, then after striking the floor it will still move in the horizontal direction in which I toss the ball at about the same speed. However, the ball will bounce upward at about the same speed it was moving downward when it hit the floor. The net result is that the ball's direction of motion is the same angle it made with a normal to the floor prior to hitting the floor.

I wish we could upload graphics to illustrate our work.

Jagella

9. Originally Posted by kojax
What I've found tutoring people through lower level math is that the best way to get them to understand it is to let them figure out the concept first, even if they get the wording wrong. Just let them get the wording wrong.

Once they understand the concept, then afterwards you explain to them that they've been using the wrong words and tell them what the right words are.

If you teach them in that order, even people with very low scholastic IQ can understand mathematics. If you start with the wording, it's very easy for them to become confused and give up. Think about it: how can they assign meaning to a word that describes an object they don't even understand yet? It's easier to use concepts they already understand, and build on them.
I like your explaining a method to educate people. Although I never tutored physics much, I have tutored algebra and trigonometry. I now realize that understanding the concepts, as you say, is primary. If I understand the concepts, the terminology is only important as far as my explaining the concepts to other people.

I got into that trouble in my opening post. Some members here took issue with my using the word "vector" to describe a ray of light. Although I realize that light rays are not normally defined as vectors, they do have direction, of course.

In any case, I believe that investigating physical phenomena for myself is very helpful in understanding them. If I wish to discover new laws of physics, for instance, then there will be nobody to explain them to me. I must figure them out for myself. Applying thought experiments, mathematics, and visual aids are very helpful in understanding physics--both established and yet to be discovered.

Jagella

10. Originally Posted by Jagella

In any case, I believe that investigating physical phenomena for myself is very helpful in understanding them. If I wish to discover new laws of physics, for instance, then there will be nobody to explain them to me. I must figure them out for myself. Applying thought experiments, mathematics, and visual aids are very helpful in understanding physics--both established and yet to be discovered.

Jagella
Just take care you don't waste too much of your time rediscovering.

11. Originally Posted by kojax
Just take care you don't waste too much of your time rediscovering.
We rediscover all the time; it's what we call "learning." Being the first person to discover is a bit overrated, in my opinion.

Jagella

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