In Chapter 16 you learned that light is an electromagnetic wave. We can describe the propagation of light waves by considering the paths that the wave fronts follow. We do this by using geometrical constructions called rays that are drawn perpendicular to the wave front. Indeed, you can understand how a great many optical devices work by merely considering these rays and not delving into the details of the wave nature of light.

When light rays strike a surface such as the face of a mirror, they are reflected back from the surface according to a very simple law of reflection: the angle that the ray makes with a line drawn perpendicular to the surface when it comes toward the reflecting surface (the angle of incidence) is equal to the angle that the reflected ray (the angle of reflection) makes with the perpendicular to the surface. In a sense the behavior of light rays upon reflection is quite similar to that of a rubber ball bounced upon the floor for it, too, has the angle of incidence equal to the angle of reflection.

Your brain is unable to determine whether the light rays that reached your eye came directly from an object or were reflected from a surface such as a mirror unless some additional information is provided, e.g. you see the outer edges of the mirror in front of you. Your brain also assumes that the light rays traveled in a straight line directly from the object to your eye. Thus when we trace the light rays that are reflected from a mirror back through the mirror, as in Figures 17.5 and 17.6 in the text, we find that they intersect behind the mirror, and we think that is where they originated. The location of the intersection of the rays is the location of an image of the object and not the location of the object itself. In the case of a plane mirror, the image formed is a virtual image, because the light rays do not actually reach the location where the image is formed. No energy passes through the location of the image.

An image is described as a real image when the light rays actually pass through the location of the image such as is the case with many, but not all, lens configurations. Lenses are made of materials such as glass that allows light to pass through, but the speed of light is slower in the material than it is in a vacuum. The result of this difference in speed is a bending of the path of the light ray from the straight-line path it would have had in a vacuum. This behavior is described in terms of the index of refraction, n, which is the ratio of the speed of light in a vacuum, c , to the speed of light in the material of interest, v , n = c / v.

For a lens and for mirrors the focal point is the point of intersection for the rays that come in parallel to the axis (as shown in the text in Figures 17.15 in the text and Figure17.20 in the text) or seem to intersect (as shown in the text in Figure 17.18 in the text).

Identification of the location of the image formed by a lens can be accomplished by using three principal rays. The image is located where these rays intersect. There is nothing special about these rays, and they do not behave any differently than any other rays, but they are easy to identify and to trace, so they are used for analysis.

A ray coming from the object traveling parallel to the axis will pass through the focal point of the lens on the far side of the lens (ray 1 in Figure 17.16 in the text) ; a ray coming through the focal point on the near side of the lens comes out parallel to the axis (ray 2 in Figure 17.16 in the text); a ray coming through the center of the lens passes through the lens without being bent (ray 3 in Figure 17.16 in the text). The distance the object is from the lens, o, and the distance the image is from the lens, I, can be expressed in an equation that involves the focal length of the lens as 1 / o + 1 / i = 1 / f . The magnification of the image is calculated as m = - i / o . A negative magnification indicates that the image is inverted with respect to the object, as is the case in Figure 17.16 in the text, and a magnification greater than one means the image is larger than the object. A converging lens has a positive focal length and a diverging lens has a negative focal length.

If the image is formed by the intersection of the actual rays at a point as shown in Figure 17.16 in the text the image is called a real image, because light energy really passes through the point. A real image can be projected onto a screen. If the image is formed by the intersection of the straight line extensions of the rays that strike your eye as shown in Figure 17.17 in the text and in Figure 17.19 in the text it is called a virtual image, because no light energy actually reaches that location. A virtual image cannot be projected onto a screen.

When light rays travel from one material through another we use the law of refraction to relate the index of refraction and angle that the light ray makes with the normal to the surface in one material to those quantities in the other material. For small angles (a one per cent error is involved for 15^o using this approximation) this relationship can be written as n₁q₁@ n₂q₂. This refraction results in the bending of light rays as they pass from a medium of one index of refraction to a medium of another index of refraction. The relationship involves a product, so when light travels from a region of lower index of refraction to a region of higher index of refraction the angle must become smaller to preserve the equality, i.e. if n₂ is larger than n₁,such as would be the case for light traveling to glass from air, then q₂ must be smaller than q₁ . Light is bent toward the normal in the material with the higher index of refraction and away from the normal in the material with the lower index of refraction.

If light rays pass from a higher index of refraction material to a lower index of refraction material and the angle of incidence is such that the angle of refraction greater than 90^o would be required by the law of refraction, none of the light can exit the higher index of refraction material and it is all reflected at the surface. This phenomenon is called total internal reflection because all of the light is reflected back into the higher index of refraction material. This phenomenon is used in the optical fibers that are utilized for telephone communications and for the "light pipes" that are widely used.

As discussed in Chapter 16, red light has a longer wavelength than blue light with other colors of light having wavelengths between these extremes. Experimentally we observe that the index of refraction for blue light is greater than that for red light, so when white light consisting of all colors of light passes through a material such as glass the blue light will be bent more than the red light resulting in the separation of the colors. This is readily demonstrated with a prism which separates a beam of white light into multi-colored components. This phenomenon is called dispersion.

Whenever a beam of light passes through slits or around obstacles whose dimensions are comparable to the wavelength of light the wave phenomena of interference and diffraction can be important. If the paths traveled by two beams of light differ by exactly one half of one wavelength, as shown in Figure 17.29 on page 366 in the text, the result is destructive interference or a dark spot on the screen. If the paths differ by some multiple of a full wavelength, the waves are in phase and a bright spot is produced on the screen.