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  4. The nature of light
  5. The law of reflection

1.2 The law of reflection

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By the end of this section, you will be able to:
  • Explain the reflection of light from polished and rough surfaces
  • Describe the principle and applications of corner reflectors

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

The law of reflection    states that the angle of reflection equals the angle of incidence, or

θ r = θ i

The law of reflection is illustrated in [link] , which also shows how the angle of incidence and angle of reflection are measured relative to the perpendicular to the surface at the point where the light ray strikes.

A light ray is incident on a smooth surface and is making an angle theta i relative to a line drawn perpendicular to the surface at the point where the incident ray strikes it. The reflected light ray makes an angle theta r with the same perpendicular drawn to the surface. Both incident and reflected ray are on the same side of the surface but opposite sides of the perpendicular line.
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.

We expect to see reflections from smooth surfaces, but [link] 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 shown in [link] (a). People, clothing, leaves, and walls all 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 [link] (b). When the Moon reflects from a lake, as shown in [link] (c), a combination of these effects takes place.

The figure shown parallel light rays falling on a rough surface. The rays hit the surface at different angles to the perpendicular lines to the surface at the points of incidence, and the reflected rays get scattered in different directions.
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.
Figure a shows the rays of light from a flashlight falling on a page of paper. The light gets reflected at many angles as the surface is rough. Reflected light reaches eyes placed at many location. Figure b shows the rays of light from a flashlight falling on mirror. All of the light gets reflected at the same angle since the surface is smooth. Reflected light only reaches an eye placed so that the reflected beam hits it. An observer not at the angle of the reflected light does not see it. Figure c shows a photograph of moonlight falling on a lake. The lake’s shiny surface reflects it. A bright , slightly rippled strip of moonlight is seen reflecting from the lake on a dark background.
(a) 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. (b) A mirror illuminated by many parallel rays reflects them in only one direction, because its surface is very smooth. Only the observer at a particular angle sees the reflected light. (c) Moonlight is spread out when it is reflected by the lake, because the surface is shiny but uneven. (credit c: modification of work by Diego Torres Silvestre)

When you see yourself in a mirror, it appears that the image is actually behind the mirror ( [link] ). We see the light coming from a direction determined by the law of reflection. The angles are such that the image is exactly the same distance behind the mirror as you stand in front of 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 your imagination. Mirror images can be photographed and videotaped by instruments and look just as they do with our eyes (which are optical instruments themselves). The precise manner in which images are formed by mirrors and lenses is discussed in an upcoming chapter on Geometric Optics and Image Formation .

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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