Reflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 34.7a shows a bundle of parallel light rays reflecting from a mirror-like surface. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the simpler pictorial representation of FIGURE 34.7b. In this figure,

• The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

• A single light ray represents the entire bundle of parallel rays. This is oversimplified, but it keeps the figure and the analysis clear.

FIGURE 34.7 Specular reflection of light.

The angle ${\theta }_{\text{i}}$ between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ${\theta }_{\text{r}}$ is the angle between the reflected ray and the normal to the surface. The law of reflection, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the surface, and

2. The angle of reflection equals the angle of incidence: ${\theta }_{\text{r}}={\theta }_{\text{i}}$.

EXAMPLE 34.1 Light reflecting from a mirror

A dressing mirror on a closet door is 1.50 m tall. The bottom is 0.50 m above the floor. A bare lightbulb hangs 1.00 m from the closet door, 2.50 m above the floor. How long is the streak of reflected light across the floor?

MODEL Treat the lightbulb as a point source and use the ray model of light.

VISUALIZE FIGURE 34.8 is a pictorial representation of the light rays. We need to consider only the two rays that strike the edges of the mirror. All other reflected rays will fall between these two.

FIGURE 34.8 Pictorial representation of the light rays reflecting from a mirror.

FIGURE 34.8 Full Alternative Text

SOLVE Figure 34.8 has used the law of reflection to set the angles of reflection equal to the angles of incidence. Other angles have been identified with simple geometry. The two angles of incidence are

$$\begin{array}{ccc}\hfill {\theta }_1& =\hfill & {\text{tan}}^{-1}\left({\displaystyle \frac{0.50\text{m}}{1.00\text{m}}}\right)=26.6\text{°}\hfill \\ \hfill {\theta }_2& =\hfill & {\text{tan}}^{-1}\left({\displaystyle \frac{2.00\text{m}}{1.00\text{m}}}\right)=63.4\text{°}\hfill \end{array}$$

The distances to the points where the rays strike the floor are then

$$\begin{array}{ccc}\hfill l_1& =\hfill & {\displaystyle \frac{2.00\text{ m}}{\text{tan }{\theta }_1}}=4.00\text{ m}\hfill \\ \hfill l_2& =\hfill & {\displaystyle \frac{0.50\text{ m}}{\text{tan }{\theta }_2}}=0.25\text{ m}\hfill \end{array}$$

Thus the length of the light streak is $l_1-l_2=3.75\text{m}$.