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The Law of Reflection

Module by: OpenStax College. E-mail the author

Summary:

  • 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 Figure 1, 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 Figure 2 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 Figure 3. 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 Figure 4. When the moon reflects from a lake, as shown in Figure 5, a combination of these effects takes place.

Figure 1: The law of reflection states that the angle of reflection equals the angle of incidence— θr=θiθr=θi. The angles are measured relative to the perpendicular to the surface at the point where the ray strikes the surface.
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.
Figure 2: 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.
Parallel light rays falling on a rough surface get scattered at different angles.
Figure 3: 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.
Light from a flashlight falls on a sheet of paper and the light gets reflected at different angles as the surface is rough.
Figure 4: 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.
A flashlight casting light on a mirror, which is smooth; the mirror reflects light only in one direction at a particular angle.
Figure 5: Moonlight is spread out when it is reflected by the lake, since the surface is shiny but uneven. (credit: Diego Torres Silvestre, Flickr)
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.

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

The Law of Reflection:

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 Figure 6. 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.

Figure 6: 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.
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.

Take-Home Experiment: Law of Reflection:

Take a piece of paper and shine a flashlight at an angle at the paper, as shown in Figure 3. Now shine the flashlight at a mirror at an angle. Do your observations confirm the predictions in Figure 3 and Figure 4? Shine the flashlight on various surfaces and determine whether the reflected light is diffuse or not. You can choose a shiny metallic lid of a pot or your skin. Using the mirror and flashlight, can you confirm the law of reflection? You will need to draw lines on a piece of paper showing the incident and reflected rays. (This part works even better if you use a laser pencil.)

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

Exercise 1

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

Exercise 1

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.

Figure 7: A corner reflector sends the reflected ray back in a direction parallel to the incident ray, independent of incoming direction.
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.

Exercise 2

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 2θ2θ size 12{2f} {} when the mirror is rotated by an angle θθ size 12{f} {}.

Exercise 3

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

Figure 8: A flat mirror neither converges nor diverges light rays. Two rays continue to diverge at the same angle after reflection.
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.

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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