Refraction is
the bending of the path of a light wave as it passes across the boundary
separating two media. Refraction is caused by the change in speed experienced
by a wave when it changes medium.
consider
a hemi-cylindrical dish filled with water. Suppose that a laser beam is
directed towards the flat side of the dish at the exact center of the dish. The
angle of incidence can be measured at the point of incidence. This ray will
refract, bending towards the normal (since the light is passing from a medium
in which it travels fast into one in which it travels slow - FST). Once
the light ray enters the water, it travels in a straight line until it reaches
the second boundary. At the second boundary, the light ray is approaching along
the normal to the curved surface (this stems from the geometry of circles). The
ray does not refract upon exiting since the angle of incidence is 0-degrees
The
ray of laser light therefore exits at the same angle as the refracted ray of
light made at the first boundary. These two angles can be measured and
recorded. The angle of incidence of the laser beam can be changed to 5-degrees
and new measurements can be made and recorded. This process can be repeated
until a complete data set of accurate values has been collected. The data below
show a representative set of data for such an experiment.
An
inspection of the data above reveals that there is no clear linear relationship
between the angle of incidence and the angle of refraction. For example, a
doubling of the angle of incidence from 40 degrees to 80 degrees does not
result in a doubling of the angle of refraction. Thus, a plot of this data
would not yield a straight line. If however, the sine of the angle of incidence
and the sine of the angle of refraction were plotted, the plot would be a
straight line, indicating a linear relationship between the sines of the
important angles. If two quantities form a straight line on a graph, then a
mathematical relationship can be written in y = m*x + b form. A plot of the sine of the angle
of incidence vs. the sine of the angle of refraction is shown below.
The equation relating the
angles of incidence (Θi) and the angle of
refraction (Θr) for light passing from
air into water is given as
Observe
that the constant of proportionality in this equation is 1.33 -the index of refraction value of
water.
Perhaps it's just a coincidence. But if the semi-cylindrical dish full of water
was replaced by a semi-cylindrical disk of Plexiglas, the constant of
proportionality would be 1.51 - the index of refraction value of
Plexiglas. This
is not just a coincidence. The same pattern would result for light traveling
from air into any material. Experimentally, it is found that for a ray of light
traveling from air into some material, the following equation can be written.
where nmaterial = index of refraction of the material
This study of the refraction of light as it crosses from one material
into a second material yields a general relationship between the sines of the
angle of incidence and the angle of refraction. This general
relationship is expressed by the following equation:
where Θi ("theta i") = angle of incidence
Θr ("theta r") = angle of refraction
ni = index of refraction of the incident medium
nr = index of refraction of the refractive
medium
This relationship between
the angles of incidence and refraction and the indices of refraction of the two
media is known as Snell's Law. Snell's law applies to the
refraction of light in any situation, regardless of what the two media are.