Mirrors for AP Physics B
Practice problems for these concepts can be found at:
Okay, time to draw some pictures. Let's start with plane mirrors.
The key to solving problems that involve plane mirrors is that the angle at which a ray of light hits the mirror equals the angle at which it bounces off, as shown in Figure 24.3.
In other words—or, more accurately, "in other symbols"—θi = θr, where θi is the incident2 angle, and θr is the reflected angle.
So, let's say you had an arrow, and you wanted to look at its reflection in a plane mirror. We'll draw what you would see in Figure 24.4.
The image of the arrow that you would see is drawn in Figure 24.4 in dotted lines. To draw this image, we first drew the rays of light that reflect from the top and bottom of the arrow to your eye. Then we extended the reflected rays through the mirror.
Whenever you are working with a plane mirror, follow these rules:
- The image is upright. Another term for an upright image is a virtual image.
- The image is the same size as the original object. That is, the magnification, m, is equal to 1.
- The image distance, di, equals the object distance, do.
A more challenging type of mirror to work with is called a spherical mirror. Before we draw our arrow as it looks when reflected in a spherical mirror, let's first review some terminology (this terminology is illustrated in Figure 24.5).
A spherical mirror is a curved mirror—like a spoon—that has a constant radius of curvature, r. The imaginary line running through the middle of the mirror is called the principal axis. The point labeled "C," which is the center of the sphere, lies on the principal axis and is located a distance r from the middle of the mirror. The point labeled "F" is the focal point, and it is located a distance f, where f = (r/2), from the middle of the mirror. The focal point is also on the principal axis. The line labeled "P" is perpendicular to the principal axis.
There are several rules to follow when working with spherical mirrors. Memorize these.
- Incident rays that are parallel to the principal axis reflect through the focal point.
- Incident rays that go through the focal point reflect parallel to the principal axis.
- Any points that lie on the same side of the mirror as the object are a positive distance from the mirror. Any points that lie on the other side of the mirror are a negative distance from the mirror.
That last rule is called the "mirror equation." (You'll find this equation to be identical to the "lensmaker's equation" later.)
To demonstrate these rules, we'll draw three different ways to position our arrow with respect to the mirror. In the first scenario, we'll place our arrow on the principal axis, beyond point "C," as shown in Figure 24.6.
Notice that the image here is upside down. Whenever an image is upside down, it is called a real image. A real image can be projected onto a screen, whereas a virtual image cannot.3
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