Geometric Optics, Vision and Optical Instruments
65 The Law of Reflection
Reflection of Light
Whenever you look into a mirror, notice sunlight reflecting from a calm lake, or read words printed on a page, you are observing the reflection of light. Reflection is one of the most common optical phenomena in everyday life and is essential to many technologies, from bathroom mirrors and automobile headlights to astronomical telescopes and medical endoscopes.
When a ray of light strikes a surface, it changes direction according to a simple geometric rule known as the law of reflection. The angles involved are measured relative to a line called the normal, which is an imaginary line drawn perpendicular to the surface at the point where the light strikes it. As shown in Figure 65.1, the angle between the incoming ray and the normal is called the angle of incidence, while the angle between the reflected ray and the normal is called the angle of reflection.
The appearance of the reflected light depends strongly on the smoothness of the reflecting surface. If the surface is smooth compared with the wavelength of light, parallel rays remain parallel after reflection. This type of reflection is called specular reflection and produces sharp images, such as those seen in mirrors.
If the surface is rough on the scale of the wavelength of light, each tiny part of the surface has a different orientation. Although the law of reflection still applies locally at every point, the reflected rays leave in many different directions. This process is called diffuse reflection.
Diffuse reflection is the reason we can see most everyday objects from many different viewing angles. A sheet of paper, a person's skin, clothing, leaves, walls, and most biological tissues all have microscopic surface irregularities that scatter light in many directions.
Mirrors behave differently because their surfaces are extremely smooth. Nearly all of the reflected rays travel in one well-defined direction, allowing mirrors to produce clear images rather than simply reflecting light diffusely.
Many natural surfaces are neither perfectly smooth nor completely rough. For example, the surface of a lake appears smooth on a calm day but contains small waves and ripples. As a result, light from the Moon or the Sun is reflected over a range of directions, producing the familiar shimmering path of light across the water.
Law of Reflection
The angle of reflection is always equal to the angle of incidence. Both angles are measured relative to the normal to the reflecting surface.
Virtual Images in Plane Mirrors
When you stand in front of a mirror, your image appears to be located behind the mirror even though no light actually travels there. Your brain assumes that light travels in straight lines and therefore traces the reflected rays backward to a point behind the mirror. This apparent source of light is called a virtual image.
For a plane mirror, the virtual image is located exactly the same distance behind the mirror as the object is in front of it. Although the image cannot be projected onto a screen, it can be photographed because cameras detect the same reflected rays that enter your eyes.
This property explains why mirrors make rooms appear larger and why mirrors are widely used in healthcare settings, including dental mirrors, surgical mirrors, and optical instruments that help clinicians observe regions that would otherwise be difficult to see.
Take-Home Experiment: Exploring the Law of Reflection
Use a flashlight and a sheet of white paper to investigate how different surfaces reflect light.
- Shine a flashlight at an angle onto a sheet of paper, as shown in Figure 65.3. Observe how the reflected light spreads in many directions.
- Repeat the experiment using a flat mirror, as shown in Figure 65.4. Notice that the reflected light is concentrated into a single direction instead of being scattered.
- Compare the reflection from several everyday objects, such as:
- a shiny metal pot lid,
- your skin,
- a book cover,
- a sheet of paper, and
- a mirror.
Classify each surface as producing primarily specular reflection (mirror-like) or diffuse reflection.
- To test the law of reflection, place a mirror on a sheet of paper and shine a flashlight (or, even better, a low-power laser pointer) at an angle. Trace the incident and reflected rays on the paper and measure their angles relative to the normal. Do your measurements confirm that the angle of incidence equals the angle of reflection?
Section Summary
- The law of reflection states that the angle of reflection is equal to the angle of incidence, with both angles measured relative to the normal to the surface.
- Smooth surfaces produce specular reflection, allowing mirrors to form clear images.
- Rough surfaces produce diffuse reflection, scattering light in many directions and allowing objects such as paper, clothing, and skin to be seen from almost any viewing angle.
- A plane mirror forms a virtual image that appears the same distance behind the mirror as the object is in front of it.
- Mirror images can be recorded by cameras and other optical instruments in the same way they are observed by the human eye.
Conceptual Questions
- Using the law of reflection, explain how face powder reduces the shine from a person's skin. What type of reflection is responsible for this effect?
Problems & Exercises
- Show that when light reflects from two mirrors that meet at a right angle, the outgoing ray is parallel to the incoming ray, as illustrated in Figure 65.7.
Figure 65.7: A corner reflector sends the reflected ray back in a direction parallel to the incident ray, regardless of the incoming direction. - Light shows that use lasers often employ rotating mirrors to sweep beams across a stage. Show that a light ray reflected from a mirror changes direction by [latex]2\theta[/latex] when the mirror is rotated through an angle [latex]\theta[/latex].
- A plane mirror neither converges nor diverges light. To demonstrate this, consider two rays originating from the same point and diverging by an angle [latex]\theta[/latex]. Show that after reflecting from a plane mirror, the angle between the reflected rays remains [latex]\theta[/latex], as illustrated in Figure 65.8.
Figure 65.8: A plane mirror neither converges nor diverges light rays. Two rays continue to diverge at the same angle after reflection.
Glossary
- mirror
- a smooth surface that reflects light in a predictable direction, allowing clear images to be formed
- law of reflection
- the principle stating that the angle of reflection is equal to the angle of incidence, with both angles measured relative to the normal to the surface
- specular reflection
- reflection from a smooth surface in which parallel incident rays remain parallel after reflection, producing a clear image
- diffuse reflection
- reflection from a rough surface that scatters light in many directions, allowing an object to be seen from many viewing angles
- angle of incidence
- the angle between an incoming light ray and the normal (perpendicular) to the surface at the point of incidence
- angle of reflection
- the angle between a reflected light ray and the normal to the surface, equal to the angle of incidence
- normal
- an imaginary line drawn perpendicular to a surface at the point where a light ray strikes
- virtual image
- an image that appears to come from a location where light rays do not actually converge, such as the image seen behind a plane mirror
a smooth surface that reflects light in a predictable direction, allowing clear images to be formed
the principle stating that the angle of reflection is equal to the angle of incidence, with both angles measured relative to the normal to the surface
reflection from a smooth surface in which parallel incident rays remain parallel after reflection, producing a clear image
reflection from a rough surface that scatters light in many directions, allowing an object to be seen from many viewing angles
the angle between an incoming light ray and the normal (perpendicular) to the surface at the point of incidence
the angle between a reflected light ray and the normal to the surface, equal to the angle of incidence
an imaginary line drawn perpendicular to a surface at the point where a light ray strikes
an image that appears to come from a location where light rays do not actually converge, such as the image seen behind a plane mirror
