The Law of Reflection, Geometric Optics | College Physics 2e

Learning objectives

Learning Objectives

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

Explain reflection of light from polished and rough surfaces.

Whenever we look into a mirror, or squint at sunlight glinting from a lake, we are seeing a reflection. When you look at this page, too, you are seeing light reflected from it. Large telescopes use reflection to form an image of stars and other astronomical objects.

The law of reflection is illustrated in import-auto-id2543500, which also shows how the angles are measured relative to the perpendicular to the surface at the point where the light ray strikes. We expect to see reflections from smooth surfaces, but import-auto-id805516 illustrates how a rough surface reflects light. Since the light strikes different parts of the surface at different angles, it is reflected in many different directions, or diffused. Diffused light is what allows us to see a sheet of paper from any angle, as illustrated in import-auto-id3190594. Many objects, such as people, clothing, leaves, and walls, have rough surfaces and can be seen from all sides. A mirror, on the other hand, has a smooth surface (compared with the wavelength of light) and reflects light at specific angles, as illustrated in import-auto-id2732729. When the moon reflects from a lake, as shown in import-auto-id2749596, a combination of these effects takes place.

View original figure (external; image not reproduced in this text edition)

Original figure description: A light ray is incident on a smooth surface and is falling obliquely, making an angle theta i relative to a perpendicular line drawn to the surface at the point where the incident ray strikes. The light ray gets reflected making an angle theta r with the same perpendicular drawn to the surface.

The law of reflection states that the angle of reflection equals the angle of incidence—

θ_{r} = θ_{i}

. The angles are measured relative to the perpendicular to the surface at the point where the ray strikes the surface.

View original figure (external; image not reproduced in this text edition)

Original figure description: Parallel light rays falling on a rough surface get scattered at different angles.

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

View original figure (external; image not reproduced in this text edition)

Original figure description: Light from a flashlight falls on a sheet of paper and the light gets reflected at different angles as the surface is rough.

When a sheet of paper is illuminated with many parallel incident rays, it can be seen at many different angles, because its surface is rough and diffuses the light.

View original figure (external; image not reproduced in this text edition)

Original figure description: A flashlight casting light on a mirror, which is smooth; the mirror reflects light only in one direction at a particular angle.

A mirror illuminated by many parallel rays reflects them in only one direction, since its surface is very smooth. Only the observer at a particular angle will see the reflected light.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark night is lit by moonlight. The moonlight is falling on the lake and as it hits, the lake’s shiny surface reflects it. A bright strip of moonlight is seen reflecting from the lake on a dark background reflecting the night sky.

Moonlight is spread out when it is reflected by the lake, since the surface is shiny but uneven. (credit: Diego Torres Silvestre, Flickr)

The law of reflection is very simple: The angle of reflection equals the angle of incidence.

When we see ourselves in a mirror, it appears that our image is actually behind the mirror. This is illustrated in import-auto-id2759160. 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 as we stand away from the mirror. If the mirror is on the wall of a room, the images in it are all behind the mirror, which can make the room seem bigger. Although these mirror images make objects appear to be where they cannot be (like 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 with our eyes (optical instruments themselves). The precise manner in which images are formed by mirrors and lenses will be treated in later sections of this chapter.

View original figure (external; image not reproduced in this text edition)

Original figure description: A girl stands in front of a mirror and looks into the mirror for her image. The light rays from her feet and head fall on the mirror and get reflected following the law of reflection: the angle of incidence theta is equal to the angle of reflection theta.

Our image in a mirror is behind the mirror. The two rays shown are those that strike the mirror at just the correct angles to be reflected into the eyes of the person. The image appears to be in the direction the rays are coming from when they enter the eyes.

Test Prep for AP Courses

An object is 2 meters in front of a flat mirror. Ray 1 from the object travels in a direction toward the mirror and normal to the mirror’s surface. Ray 2 from the object travels at an angle of 5° from the direction of ray 1, and it also reflects off the mirror’s surface. At what distance behind the mirror do these two reflected rays appear to converge to form an image?

0.2 m
0.5 m
2 m
4 m

(c)

Two light rays originate from object A, at a distance of 50 cm in front of a flat mirror, diverging at an angle of 10°. Both of the rays strike a flat mirror and reflect. Two light rays originate from object B, at a distance of 50 cm in front of a convex mirror, diverging at an angle of 10°. Both of the rays strike the convex mirror and reflect. For which object do the reflected rays appear to converge behind the mirror closer to the surface of the mirror, thus forming a closer (larger) image? Explain with the help of a sketch or diagram.

Section Summary

The angle of reflection equals the angle of incidence.
A mirror has a smooth surface and reflects light at specific angles.
Light is diffused when it reflects from a rough surface.
Mirror images can be photographed and videotaped by instruments.

Conceptual Questions

Using the law of reflection, explain how powder takes the shine off of a person’s nose. What is the name of the optical effect?

Problems & Exercises

Show that when light reflects from two mirrors that meet each other at a right angle, the outgoing ray is parallel to the incoming ray, as illustrated in the following figure.

View original figure (external; image not reproduced in this text edition)

Original figure description: Two mirrors meet each other at a right angle. An incoming ray of light is reflected by one mirror and then the other, such that the outgoing ray is parallel to the incoming ray.

A corner reflector sends the reflected ray back in a direction parallel to the incident ray, independent of incoming direction.

Light shows staged with lasers use moving mirrors to swing beams and create colorful effects. Show that a light ray reflected from a mirror changes direction by $2 θ$ when the mirror is rotated by an angle $θ$ .

A flat mirror is neither converging nor diverging. To prove this, consider two rays originating from the same point and diverging at an angle $θ$ . Show that after striking a plane mirror, the angle between their directions remains $θ$ .

View original figure (external; image not reproduced in this text edition)

Original figure description: Light rays diverging from a point at an angle theta fall on a mirror at two different places and their reflected rays diverge. When the reflected rays are extended backwards from their points of reflection, they meet at a point behind the mirror, where they diverge from each other at the same angle theta.

A flat mirror neither converges nor diverges light rays. Two rays continue to diverge at the same angle after reflection.

Glossary

mirror: smooth surface that reflects light at specific angles, forming an image of the person or object in front of it
law of reflection: angle of reflection equals the angle of incidence

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