Curved Mirrors and the Law of Reflection
Most recent answer: 10/22/2007
Q:
Do convex and concave mirrors follow the law of reflection? How could you find out?
- Tamara (age 13)
- Tamara (age 13)
A:
Hi Tamara!
First of all, I've gotta say 'thumbs up!' to your parents on their choice of names! ;)
As for your question, I'm assuming that by "the law of reflection" that you mean Snell's Law, where light bounces off a flat mirror at the same angle that it hits it at, that is if it comes in at right angles to the surface it bounces off the same way. If it comes in at say 30° from the surface it bounces off at 30° from the surface.
And the answer is, yes! Curved mirrors like convex and concave mirrors do follow this law. Or at least they do in a way... this happens when you make a certain approximation - that if you zoom in really really close on a curved mirror, it's basically flat. In math terms, this is saying that a curved surface is "locally linear". It's kind of like this:
So why do we care if a curved mirror is basically flat when you look really closely? Well, if you think about a single ray of light hitting the mirror, it only hits a very very small spot. And if we think of each little spot on the mirror as being basically flat, then each ray of light that hits the mirror acts like it's hitting a flat mirror.
When we draw light rays on a piece of paper, we usually use something called a 'tangent line'. This is just a straight line, drawn right up against the curve of the mirror. A tangent line is kind of like what the curve would look like really really close up. This way we can use Snell's law to solve problems with curved mirrors:
-Tamara
First of all, I've gotta say 'thumbs up!' to your parents on their choice of names! ;)
As for your question, I'm assuming that by "the law of reflection" that you mean Snell's Law, where light bounces off a flat mirror at the same angle that it hits it at, that is if it comes in at right angles to the surface it bounces off the same way. If it comes in at say 30° from the surface it bounces off at 30° from the surface.
And the answer is, yes! Curved mirrors like convex and concave mirrors do follow this law. Or at least they do in a way... this happens when you make a certain approximation - that if you zoom in really really close on a curved mirror, it's basically flat. In math terms, this is saying that a curved surface is "locally linear". It's kind of like this:
So why do we care if a curved mirror is basically flat when you look really closely? Well, if you think about a single ray of light hitting the mirror, it only hits a very very small spot. And if we think of each little spot on the mirror as being basically flat, then each ray of light that hits the mirror acts like it's hitting a flat mirror.
When we draw light rays on a piece of paper, we usually use something called a 'tangent line'. This is just a straight line, drawn right up against the curve of the mirror. A tangent line is kind of like what the curve would look like really really close up. This way we can use Snell's law to solve problems with curved mirrors:
-Tamara
(published on 10/22/2007)
Follow-Up #1: Convex and Concave Mirrors and Lenses
Q:
Convex mirrors cause light to spread out, concave mirrors cause light to go in and create a focal point. But lenses work the opposite way: concave lenses spread the light out, convex lenses focus the light. WHY IS THAT? Why don't they work in the SAME way as mirrors, instead of the opposite way?
- Dana Aldinger
Monty Middle School, Coquitlam, BC, Canada
- Dana Aldinger
Monty Middle School, Coquitlam, BC, Canada
A:
Dana,
Thanks for your question. The reason that mirrors and lenses behave so differently is that light passes though lenses but bounces off mirrors.
When light hits a piece of glass (or any other clear material) it will go though it. The direction of the light can change, however. If a ray of light enters some glass in a direction that is not perpendicular to the surface, it will be bent so that inside the glass the direction the light travels is closer to being perpendicular to the surface. You can think of this as the light being bent away from the surface of the glass once its inside. This is called refraction.
When light hits a convex (bulging) lens this results in focusing since the light is all refracted toward a line running through the center of the lens. (See the picture I included below).
Reflection is easier to understand, and works just the opposite. When light hits a mirror it bounces off the surface. This works in the same way that a ball bounces off the floor. If you throw a ball straight down at the floor, it will bounce straight back up. If you throw it at some angle it will bounce away from the floor at he same angle. If you throw bouncy balls at a concave shape (a bowl) they will tend to bounce toward the middle (just like a concave mirror makes light bounce toward the middle, which is focusing). If you throw balls at a convex shape (a dome) they will bounce out all over the place, just like convex mirrors spread light out. (Again, see the picture)
I hope this helps.
MS
[Whoops, an incorrect picture is being replaced, see entry below.]
Thanks for your question. The reason that mirrors and lenses behave so differently is that light passes though lenses but bounces off mirrors.
When light hits a piece of glass (or any other clear material) it will go though it. The direction of the light can change, however. If a ray of light enters some glass in a direction that is not perpendicular to the surface, it will be bent so that inside the glass the direction the light travels is closer to being perpendicular to the surface. You can think of this as the light being bent away from the surface of the glass once its inside. This is called refraction.
When light hits a convex (bulging) lens this results in focusing since the light is all refracted toward a line running through the center of the lens. (See the picture I included below).
Reflection is easier to understand, and works just the opposite. When light hits a mirror it bounces off the surface. This works in the same way that a ball bounces off the floor. If you throw a ball straight down at the floor, it will bounce straight back up. If you throw it at some angle it will bounce away from the floor at he same angle. If you throw bouncy balls at a concave shape (a bowl) they will tend to bounce toward the middle (just like a concave mirror makes light bounce toward the middle, which is focusing). If you throw balls at a convex shape (a dome) they will bounce out all over the place, just like convex mirrors spread light out. (Again, see the picture)
I hope this helps.
MS
[Whoops, an incorrect picture is being replaced, see entry below.]
(published on 10/22/2007)
Follow-Up #2: Wrong lens diagram
Q:
Upper right diagram is wrong! That is still a convex lens, thicker in the middle, which makes rays converge.
- Dave (age 42)
Livonia, MI
- Dave (age 42)
Livonia, MI
A:
Yipes! Thank you for catching that!
I'll scrounge around and find a correct set of figures.
Like these, from
I'll scrounge around and find a correct set of figures.
Like these, from
(published on 05/03/2013)