Introduction to Mirrors

Hello and welcome to this video for Physics 132 where I will introduce some basics of mirrors. This video will introduce you to another type of optical element, a curved mirror. However I should point out that this mirror sort of assumes that you have already watched the video “Introduction to lenses,” if you have not already watched that video please go do that first as connections to lenses will be made throughout this video. By the end of this video you should be able to Look at a mirror and say if it’s either converging or diverging and moreover you should Know the connection between a mirrors radius and its focal length. So, let’s talk about mirrors. Just like lenses, curved mirrors can be used to focus light to a point or spread it out. Mirrors come in two basic shapes, we have concave mirrors such as this mirror on the left, which has a concave shape bending towards the light source, or we can have a convex mirror that sort of curves away from the light source. Now concave mirrors are known also as converging mirrors and dot convex mirrors are also known as diverging mirrors. To see why let’s look at the light rays as they come out of these blue boxes and interact with the mirrors. Now the light rays are kind of hard to see so I’m gonna highlight them with some red lines So out of the blue box near the top we get a red light beam. We can apply the law of reflection to the point where the light beam meets the mirror and see that the light beam will pass out in sort of this type of direction. Now if we take a second light beam from say the bottom of the box, and again apply the law of reflection to the point where the light beam hits the mirror, it will bounce out something like this. We can see that the two light rays have been converged to a point. So, in this sense the concave converging mirror is functioning similar to a converging lens, it’s taking incoming parallel light rays and converging them to a point. A common example of this particular type of mirror in use is the shaving mirror or makeup mirror that you might have in your bathroom that lets you see your face a little bit larger. On the flip side a convex mirror takes the incoming light rays and causes them to spread out. Now just as we did with the lens if we sort of imagine what someone to the left of the box sees. Well, our eyes kind of assume that light travels in straight lines so we trace the rays back and the light rays appear to originate from a point behind the mirror. So in this case, a convex mirror is providing a very similar function to a diverging lens, taking incoming parallel light and producing outgoing light that’s diverging as if it came from some point. You can see convex mirrors quite frequently as security mirrors in buildings. All the mirrors we will talk about in this particular class will be called spherical mirrors, meaning that the mirror is part of a sphere. And, while most mirrors are not actually spherical, it turns out that studying spherical mirrors is a very good approximation for most real curved mirrors. When we say that the mirror is part of a sphere here’s sort of what we mean. So in this picture we have a big sphere and we can see that the mirrors convex on the left and concave on the right, the black line is the reflective surface form part of this sphere. So now let’s talk about focal lengths and focal points for mirrors. So just like lenses the focal point is the point where the photons either converge to or appear to emanate from. So for the concave mirror, which is converging on the left, we’ve already seen that light comes in and converges to some point, this is known as the focal point. For the diverging mirror, the light comes in and bounces off, light comes in and bounces off, and the light appears to emanate from some point behind the mirror, so this would be the focal point for this diverging mirror. Unlike lenses, mirrors only have a single focal point and this basically stems from the fact that light can go through a lens from either direction, I can put the light on either side of the lens and the light will go through. For a mirror on the other hand, a mirror only has one reflective surface so there’s only one side that will act as a mirror and therefore mirrors only have a single focal point. As with lenses, the focal length, which we designate f, is the distance in meters from the surface of the mirror, to the focal point. So for the converging lens on the left, this blue arrow represents the focal length f and for the diverging mirror we have this focal length on the right. And just as with lenses, converging mirrors have a positive focal length and diverging mirrors have a negative focal length. So you can start to see some similarity between mirrors and lenses. When things are converging you have positive focal lengths, when things are diverging you have negative focal lengths. Now let’s talk a little bit about focal lengths and the radius of curvature. I want you to remember that all the mirrors we will be talking about here are parts of a sphere. And so we need two new terms we need the center of curvature, so that represents the center of the sphere of which the mirror is apart and the radius of curvature, and the radius of curvature, is exactly that, it’s the radius of which the mirror is a part. The focal length of any spherical mirror is half the radius, so here on the right we have a concave mirror on the top with positive focal length and a convex mirror on the bottom with negative focal length, the distance r is the radius of the sphere of which this mirror is a part and the focal length is half that radius. So in summary Mirrors, like lenses, can be used to focus or spread out light. Just as with lenses, mirrors have a focal point where the photons either appear to converge to or emanate from. However mirrors only have one focal point as opposed to two for lenses which is basically due to the fact that you can’t shine light through a mirror. Like lenses, mirrors have a focal length and this focal length is measured from the surface of the mirror to the focal point. The signs for focal length are the same for lenses and mirrors, for converging focal lengths are positive and for diverging focal lengths are negative. Finally the mirrors that we will deal with in this class are parts of spheres and will have a focal length that is one half of the radius of the associated sphere, which we were right mathematically as f=r/2. This concludes this video.

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