From http://physics.bu.edu/~duffy/PY106/Reflection.html by Hannah Sevian, excluding middle part on
spherical mirrors and http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/opt/wtr/rnbw/frm.rxml by Stephen
Hall of WW2010 University of Illinois
The reflection and refraction of light
Rays and wave fronts
Light is a very complex phenomenon, but in many situations its behavior can be understood with a
simple model based on rays and wave fronts. A ray is a thin beam of light that travels in a straight line.
A wave front is the line (not necessarily straight) or surface connecting all the light that left a source at
the same time. For a source like the Sun, rays radiate out in all directions; the wave fronts are spheres
centered on the Sun. If the source is a long way away, the wave fronts can be treated as parallel lines.
Rays and wave fronts can generally be used to represent light when the light is interacting with objects
that are much larger than the wavelength of light, which is about 500 nm. In particular, we'll use rays
and wave fronts to analyze how light interacts with mirrors and lenses.
The law of reflection
Objects can be seen by the light they emit, or, more often, by the light they reflect. Reflected light obeys
the law of reflection, that the angle of reflection equals the angle of incidence.
For objects such as mirrors, with surfaces so smooth that any hills or valleys on the surface are smaller
than the wavelength of light, the law of reflection applies on a large scale. All the light travelling in one
direction and reflecting from the mirror is reflected in one direction; reflection from such objects is
known as specular reflection.
Most objects exhibit diffuse reflection, with light being reflected in all directions. All objects obey the
law of reflection on a microscopic level, but if the irregularities on the surface of an object are larger
than the wavelength of light, which is usually the case, the light reflects off in all directions.
Plane mirrors
A plane mirror is simply a mirror with a flat surface; all of us use plane mirrors every day, so we've got
plenty of experience with them. Images produced by plane mirrors have a number of properties,
including:
1. the image produced is upright
2. the image is the same size as the object (i.e., the magnification is m = 1)
3. the image is the same distance from the mirror as the object appears to be (i.e., the image
distance = the object distance)
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4. the image is a virtual image, as opposed to a real image, because the light rays do not actually
pass through the image. This also implies that an image could not be focused on a screen placed
at the location where the image is.
A little geometry
Dealing with light in terms of rays is known as geometrical optics, for good reason: there is a lot of
geometry involved. It's relatively straight-forward geometry, all based on similar triangles, but we
should review that for a plane mirror.
Consider an object placed a certain distance in front of a mirror, as shown in the diagram. To figure out
where the image of this object is located, a ray diagram can be used. In a ray diagram, rays of light are
drawn from the object to the mirror, along with the rays that reflect off the mirror. The image will be
found where the reflected rays intersect. Note that the reflected rays obey the law of reflection. What
you notice is that the reflected rays diverge from the mirror; they must be extended back to find the
place where they intersect, and that's where the image is.
Analyzing this a little further, it's easy to see that the height of the image is the same as the height of the
object. Using the similar triangles ABC and EDC, it can also be seen that the distance from the object to
the mirror is the same as the distance from the image to the mirror.
Refraction
When we talk about the speed of light, we're usually talking about the speed of light in a vacuum, which
is 3.00 x 108 m/s. When light travels through something else, such as glass, diamond, or plastic, it travels
at a different speed. The speed of light in a given material is related to a quantity called the index of
refraction, n, which is defined as the ratio of the speed of light in vacuum to the speed of light in the
medium:
index of refraction : n = c / v
When light travels from one medium to another, the speed changes, as does the wavelength. The index
of refraction can also be stated in terms of wavelength:
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Although the speed changes and wavelength changes, the frequency of the light will be constant. The
frequency, wavelength, and speed are related by:
The change in speed that occurs when light passes from one medium to another is responsible for the
bending of light, or refraction, that takes place at an interface. If light is travelling from medium 1 into
medium 2, and angles are measured from the normal to the interface, the angle of transmission of the
light into the second medium is related to the angle of incidence by Snell's law :
Rainbows
an arc of concentric colored bands
A rainbow is an arc of concentric colored bands that develops
when sunlight interacts with rain drops.
A rainbow occurs when rain is falling in one portion of the sky and the sun is shining in another. For a
rainbow to be seen, the sun must be behind an observer who is facing falling rain.
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Sunlight is refracted as it enters a raindrop, which
causes the different wavelengths (colors) of visible
light to separate. Longer wavelengths of light (red) are
bent the least while shorter wavelengths (violet) are
bent the most.
If the angle between the refracted light and the normal to the drop surface is greater than a critical angle,
the light reflects off the back of the drop.
The critical angle for water (which would apply to raindrops) is 48
degrees (relative to the normal). Therefore, if light strikes the back of a
raindrop at an angle greater than 48 degrees, it will be reflected back. If
the angle is smaller than 48 degrees, the light will simply pass on
through.
The reflected light is refracted as it exits the drop. Violet light (bending the most) emerges at an angle of
40 degrees relative to the incoming sunlight while red light (bending the least) exits the drop at an angle
of 42 degrees. Other colors of the rainbow leave a raindrop at angles somewhere in between. According
to Descartes' calculations using laws of optics, the three stage refraction-reflection-refraction pattern that
light undergoes when passing through a raindrop produces a concentration of outgoing rays along a line
that is 42 degrees above the head of an observer's shadow. This concentration of light rays is the
rainbow that we see.
Since only one color of light is observed from each raindrop, an
incredible number of raindrops is required to produce the
magnificent spectrum of colors that are characteristic of a
rainbow.
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