Now let's transition to Optics. In optics, we're gonna be dealing with objects and their images. We will have both real images and virtual images. Now a real image is the result of actual light passing through it. In virtual images, your eye extrapolates light passing though the image. Now in a mirror, the real image is on the same side as the object. Read full transcript
So if we had a mirror and an object, the image that's real would be on the same side of the mirror. In the lens, the opposite is true. If we have our object, the image will be on the opposite side of the lens. For virtual images, the opposite is true. In a mirror, a virtual image is on the opposite side.
And in a lens, a virtual image is on the same side. Now it's important for you to remember the spherical mirror equation, or 1 over the object distance plus 1 over the image distance, equals 1 over the focal length, which is the same as 2 over the radius of curvature. Now the thin spherical lens equation is also equal to 1/o +1/i = 1/f = 2/r. These two use the same equation.
Lastly, a magnification is given by negative image over object. So if the magnification is negative, this means that the image is upside down. If the magnification is between 0 to 1, it's going to be smaller. And if the magnification is greater than 1, it will be larger. Now mirrors involve principles of reflection. The law of reflection says that light will reflect off a surface in such a manner that the angle of incidence equals the angle of reflection.
So if you pull up a mirror, we draw the normal, we have an incoming light ray, that angle of incidence, theta, equals the angle of reflection, so that is also theta. By geometry, these two angles must also be equal. Now let's draw the reflection of an arrow in a plane mirror. In a plane mirror, we're going to find that for the object, the image will be an equal distance but on the opposite side of the mirror.
Is this image therefore real or virtual? This is going to be a virtual image cuz it's on the opposite side of the mirror. If we were to look at a light ray, it would bounce like this. Our eye would see it and extrapolate light back to this image. What is the focal length of the mirror? For this we'll want to recall the equation, 1 over object plus 1 over image equals 1 over focal length.
And we said that if this is the object distance and this is the image distance, object is just simply equal to negative image. The two are equal but in opposite directions. So we can then substitute that in. One over -1 plus 1 over i equals 1 over focal length. This tells us that 0 equals 1 over focal length.
A little way to get 0 is for focal length then to go to infinity. 1 over infinity is 0. So the focal length for a plane mirror is infinity. Which essentially makes it an infinitely large spherical mirror, which we will now discuss. Now spherical mirrors come in two general types.
The concave or converging mirror, where the reflective surface looks cave-like or converges. And the diverging mirror, a convex mirror, where it bows out. Now we can create a spherical mirror by taking a giant sphere whose inside is lined with silver to make it reflective. And then we essentially just cut out a small portion of it.
Now the distance from the center of the sphere to the wall, is the radius of curvature. This point in the middle is called the center of curvature. And half of the radius of curvature is equal to the focal length. And we want to remember these equations. 1/o +1/i =1/f, which is the same thing as 2/r.
And magnification equals -i/o.