Reflection

Section Learning Objectives

By the end of this section, you will be able to do the following:

Explain reflection from mirrors, describe image formation as a consequence of reflection from mirrors, apply ray diagrams to predict and interpret image and object locations, and describe applications of mirrors
Perform calculations based on the law of reflection and the equations for curved mirrors

Section Key Terms

angle of incidence	angle of reflection	central axis	concave mirror	convex mirror
diffused	focal length	focal point	geometric optics	law of reflection
law of refraction	ray	real image	specular	virtual image

Characteristics of Mirrors

There are three ways, as shown in Figure 16.2, in which light can travel from a source to another location. It can come directly from the source through empty space, such as from the Sun to Earth. Light can travel to an object through various media, such as air and glass. Light can also arrive at an object after being reflected, such as by a mirror. In all these cases, light is modeled as traveling in a straight line, called a ray. Light may change direction when it encounters the surface of a different material (such as a mirror) or when it passes from one material to another (such as when passing from air into glass). It then continues in a straight line—that is, as a ray. The word ray comes from mathematics. Here it means a straight line that originates from some point. It is acceptable to visualize light rays as laser rays (or even science fiction depictions of ray guns).

In view (a), a cartoon image of Earth contains a house superimposed over North America. The Sun is included above and to the right of Earth. An arrow points from the Sun’s rays to a series of lines, which represent Earth’s atmosphere, directly above the Earth. In view (b), a woman is looking out of a window at her car. Arrows show the Sun’s rays bouncing off the car and traveling as light toward the woman.

Figure 16.2 Three methods for light to travel from a source to another location are shown. (a) Light reaches the upper atmosphere of Earth by traveling through empty space directly from the source (the Sun). (b) This light can reach a person in one of two ways. It can travel through a medium, such as air or glass, and typically travels from one medium to another. It can also reflect from an object, such as a mirror.

Because light moves in straight lines, that is, as rays, and changes directions when it interacts with matter, it can be described through geometry and trigonometry. This part of optics, described by straight lines and angles, is therefore called geometric optics. There are two laws that govern how light changes direction when it interacts with matter: the law of reflection, for situations in which light bounces off matter; and the law of refraction, for situations in which light passes through matter. In this section, we consider the geometric optics of reflection.

Whenever we look into a mirror or squint at sunlight glinting from a lake, we are seeing a reflection. How does the reflected light travel from the object to your eyes? The law of reflection states: The angle of reflection, $θ_{r} θ_{r}$ , equals the angle of incidence, $θ_{i} θ_{i}$ . This law governs the behavior of all waves when they interact with a smooth surface, and therefore describe the behavior of light waves as well. The reflection of light is simplified when light is treated as a ray. This concept is illustrated in Figure 16.3, which also shows how the angles are measured relative to the line perpendicular to the surface at the point where the light ray strikes it. This perpendicular line is also called the normal line, or just the normal. Light reflected in this way is referred to as specular (from the Latin word for mirror: speculum).

We expect to see reflections from smooth surfaces, but Figure 16.4, illustrates how a rough surface reflects light. Because the light is reflected from different parts of the surface at different angles, the rays go in many different directions, so the reflected light is diffused. Diffused light allows you to read a printed page from almost any angle because some of the rays go in different directions. Many objects, such as people, clothing, leaves, and walls, have rough surfaces and can be seen from many angles. A mirror, on the other hand, has a smooth surface and reflects light at specific angles.

A smooth, flat reflective surface is shown. A dotted line drops from the top of the figure and ends when it reaches the smooth surface. This line is perpendicular to the surface; there is a 90° angle between the surface and the perpendicular line. To the left of the perpendicular line, a ray (called an “incident ray” strikes the surface at a 45° angle. This ray—the “reflective ray”—is reflected off the surface to the right of the perpendicular line, again at a 45° angle. The angle between the incident ray and the perpendicular line is θi; the angle between the perpendicular line and the reflected ray is θr.

Figure 16.3 The law of reflection states that the angle of reflection, θ_r, equals the angle of incidence, θ_i. The angles are measured relative to the line perpendicular to the surface at the point where the ray strikes the surface. The incident and reflected rays, along with the normal, lie in the same plane.

A rough surface, such as the ground, is shown. Multiple rays are striking the uneven surface and are bouncing off the ground in different directions.

Figure 16.4 Light is diffused when it reflects from a rough surface. Here, many parallel rays are incident, but they are reflected at many different angles because the surface is rough.

When we see ourselves in a mirror, it appears that our image is actually behind the mirror. We see the light coming from a direction determined by the law of reflection. The angles are such that our image is exactly the same distance behind the mirror, d_i, as the distance we stand away from the mirror, d_o. Although these mirror images make objects appear to be where they cannot be (such as behind a solid wall), the images are not figments of our imagination. Mirror images can be photographed and videotaped by instruments and look just as they do to our eyes, which are themselves optical instruments. An image in a mirror is said to be a virtual image, as opposed to a real image. A virtual image is formed when light rays appear to diverge from a point without actually doing so.

Figure 16.5 helps illustrate how a flat mirror forms an image. Two rays are shown emerging from the same point, striking the mirror, and reflecting into the observer’s eye. The rays can diverge slightly, and both still enter the eye. If the rays are extrapolated backward, they seem to originate from a common point behind the mirror, allowing us to locate the image. The paths of the reflected rays into the eye are the same as if they had come directly from that point behind the mirror. Using the law of reflection—the angle of reflection equals the angle of incidence—we can see that the image and object are the same distance from the mirror. This is a virtual image, as defined earlier.

A flat mirror is placed perpendicular to our field of view. We see the side of the mirror. A bottle is placed to the left of the mirror at distance do to the mirror. Two rays originate from the bottle, strike the mirror, and reflect to an eye that is looking at the mirror. To the right of the mirror, a virtual image of the bottle is included as a backward extrapolation of the path of the rays from the eye to the mirror. The bottle to the right of the mirror is at distance di from the mirror.

Figure 16.5 When two sets of rays from common points on an object are reflected by a flat mirror into the eye of an observer, the reflected rays seem to originate from behind the mirror, which determines the position of the virtual image.

Fun In Physics

Mirror Mazes

Figure 16.6 is a chase scene from an old silent film called The Circus, starring Charlie Chaplin. The chase scene takes place in a mirror maze. You may have seen such a maze at an amusement park or carnival. Finding your way through the maze can be very difficult. Keep in mind that only one image in the picture is real—the others are virtual.

This black-and-white still shot shows Charlie Chaplin and a thief in a maze of mirrors. Images of Chaplin and the thief appear in mirrors, within mirrors, within mirrors.

Figure 16.6 Charlie Chaplin is in a mirror maze. Which image is real?

One of the earliest uses of mirrors for creating the illusion of space is seen in the Palace of Versailles, the former home of French royalty. Construction of the Hall of Mirrors (Figure 16.7) began in 1678. It is still one of the most popular tourist attractions at Versailles.

The Hall of Mirrors at Versailles features an al fresco and gilded domed ceiling; many large, hanging crystal chandeliers; exquisite painted panels on the walls; and mirrors—lots and lots of mirrors—to give an illusion of space. Tourists are pictured roaming the Hall.

Figure 16.7 Tourists love to wander in the Hall of Mirrors at the Palace of Versailles. (credit: Michal Osmenda, Flickr)

Grasp Check

Only one Charlie in this image (Figure 16.8) is real. The others are all virtual images of him. Can you tell which is real? Hint—His hat is tilted to one side.

A grayscale image of Charlie Chaplain in a house of mirrors is shown. There are infinite images of him, His image in the foreground has his hat tilted to the left.

Figure 16.8

The virtual images have their hats tilted to the right.
The virtual images have their hats tilted to the left.
The real images have their hats tilted to the right.
The real images have their hats tilted to the left.

Watch Physics

Virtual Image

This video explains the creation of virtual images in a mirror. It shows the location and orientation of the images using ray diagrams, and relates the perception to the human eye.

Virtual image | Geometric optics | Physics | Khan Academy

Watch Physics: Virtual Image. This video explains the concept of virtual images.

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