Flat Mirrors:

Two rays are sufficient to determine the image of an object as shown in Figure 36.2 on page 1053 of Serway. Since the angle of incidence must equal the angle of reflection, can you see that the image distance q must be the same as the object distance p and that the image height h' is the same as the object height h; thus, the magnification is one?

A more complex case is shown in Figure 36.3, page 1054. Because there are two perpendicular mirrors, there are three images!

Refer back to both of these figures. In each case, the images are virtual. That means that the images are not formed by the intersection of actual rays of light and cannot therefore be formed on a screen placed at the image positions. An eye is needed to form an image, since the actual rays of light diverge after reflection from the mirror.

Curved Mirrors:

Look at Figure 36.6 on page 1055. For this spherical concave mirror, the focal length f (position not shown) is half of the radius of curvature R (position C at distance CV). The focal length is defined to be the point through which parallel incoming rays reflect (see Figure 36.9 on page 1057). But this is an approximation for spherical mirrors, since rays farther away from the principal axis reflect through a slightly different "focus". Figure 36.7 is not attempting to show the focal point, but is instead showing another effect of this spherical aberration. Parabolic mirrors do not suffer from this problem (photograph on the bottom of page 1055).

Ignoring spherical aberration, the focal point for a concave mirror can be found by allowing light from a distant object to fall on the mirror. A piece of white cardboard (screen) is moved back and forth in front of the mirror until a clear image is formed on the screen. The distance from the mirror to the screen is the focal length; twice this is the radius of curvature. Since a convex mirror cannot form a real image, this method cannot be used to find the focal length for a convexmirror which, in any case, is behind the mirror (note points F and C in Figure 36.10 on page 1058).

There are three principal rays that can be used to sketch these ray diagrams:

1) An incoming ray parallel to the principal axis is either
a) reflected through the focus, or (ray 1, Fig. 36.12a and Fig. 36.12b)
b) appears to come from the focus (ray 1, Fig. 36.12c)
2) An incoming ray that is aimed at the focus is reflected parallel to the principal axis
(ray 2 in Fig. 36.12a and Fig. 36.12c)
Or, the incoming ray can appear to be coming from the focus as in Fig. 36.12b, ray2.
3) An incoming ray that passes through the center of curvature is reflected back upon itself. (This is because it is incident at 0^o.) This is shown by rays 3 in all three cases of Fig. 36.12.

It is important to follow the sign conventions listed at the bottom of page 1058. You might want to look at my two examples, as well as Serway's:

Example 1: A Concave Mirror
Example 2: A Convex Mirror

You need not study the formulas in section 36.3, but you should study the diagram shown in Example 36.8 on page 1064, since you'll need those principles to do problem 17. (Problem 17 can be solved using ray diagrams, Snell's Law, and the approximations below.)

Approximations for small angles (usually less than 5^o):

Thin Lenses:

A lens has two surfaces at which refraction takes place. Thus it has two focal lengths. Serway goes through the derivation on page 1065 to come up with the lens makers' equation, which enables the focal length f to be computed from the index of refraction n and the two radii of curvature. He also points out that the formula involving p, q, and f is identical to that for mirrors, except for the sign conventions:

From the sign conventions for R_#, you can see that either R₁ or R₂ has to be negative. Thus, in the lens makers' equation, you had better end up adding the terms within the large parentheses!

The three principal rays are a little different for thin lenses:

1) An incoming ray parallel to the axis goes through the focus
2) A ray through the focus is bent parallel to the axis
3) A ray through the center of the lens is undeviated

When an object is used that is not a simple line, the calculations become complex. See my example: Biconvex Lens - Image Dimensions.

You should read section 36.5 for information about lens aberrations. Serway classifies them into two categories. There are a number of subcategories. Good photography and microscope images require corrections; to compensate for four or more can be quite expensive.

Here are a few diagrams that may help you visualize the concepts:
        The Fresnel lens provides strong focusing using much less glass than a conventional lens.  The diagrams show how the glass is removed (unfilled sections).  The remaining glass (filled or dark sections) is brought to the center line to form an equivalent lens.
        A little more on aberrations - spherical, chromatic, and coma.
        The two basic kinds of spherical mirrors are convex and concave.
        When the object is placed at the center of curvature of a concave mirror, the image also appears there!
        For a concave mirror, when the object is placed at the focus, reflected rays are parallel (intersect at infinity; no image).
        For a concave mirror, when the object is placed past the center of curvature, the image is real, smaller, inverted, and between the focus and the center of curvature.
        For a concave mirror, when the object is placed between the focus and the center of curvature, here's the image!
        When the object is placed inside the focus of a concave mirror, a virtual image results.
        Here's a drawing of an overhead projector - an application of mirrors and lenses.