As light goes from water into air or from glass into air or from plastic into air, the light is bent away from the normal (or perpendicular). This happens when light goes from a material where its speed is slow into a material where its speed is fast. Bending away from the normal (or perpendicular) means the angle of refraction is greater than the angle of incidence for these cases. In addition to the refracted ray, there is also some light reflected at the surface. The amount of light reflected increases as the angle of refraction increases.
For some angle of incidence, the angle of refraction-the angle
of the outgoing light-would be 90 meaning that all of the light
that passes through into the air would be grazing across the surface.
For that and all larger angles of incidence, no light will be
transmitted into the air. All the light will be reflected at the
water-air surface. This is known as total internal reflection.
The smallest angle of incidence for which this happens is known
as the critical angle. A list of critical angles
for various materials is given in Table 16.1. Figure 16.14 illustrates
this for a water-air surface where the critical angle is 49.
The critical angle depends upon the index of refraction. From
Table 16.1 you can see that diamond has a very large index of
refraction and the critical angle for diamond is relatively small.
This means light will bounce around inside a diamond more often
than with glass. Total internal reflection is important in the
design of small, hand-held binoculars. Figure 16.15 illustrates
a long telescope-a "spyglass" that you might see used
in a swashbuckling pirate movie. Such a telescope is long and
clumsy and difficult to handle. "Folding" the path of
the light between the two lenses will make the device shorter
and easier to handle. Mirrors could be used to reflect the light
back and forth and accomplish this. However, mirrors absorb five
to ten percent of the light they reflect. When you look at yourself
in a bathroom mirror this does not make any difference. But when
four reflections are involved and the image may be dim to begin
with, loss of so much light is quite important. Instead of mirrors,
we can arrange prisms so the light is reflected by total internal
reflection. And total internal reflection really is that-it is
total; there is no loss of light. Binoculars use such an arrangement
of prisms as illustrated in Figure 16.15.
Total internal reflection is important in fiber optics that are
now used for telephone communications-and for computers and television
and other forms of communications. Figure 16.16 illustrates a
light beam entering a fiber of glass or plastic. Even though the
optic fiber may bend around curves and corners, the light will
be reflected inside the optic fiber because the angles of reflection
will be greater than the critical angle. Since these reflections
are all by total internal reflection, there will be no light lost.
Total internal reflection is also important in fiber optics that
are now literally revolutionizing internal medicine. Orthoscopic
endoscopes allow an orthopedic surgeon to look behind a knee cap
with a very small incision instead of major surgery. Other endoscopes
allow all sorts of internal investigations without invasive surgery.
It is fun to describe what a scuba diver or a fish might see while underwater and looking up at a very smooth surface between the water and air. The light from the air above will be refracted so objects will appear to be somewhere other than where they "really" are. The light from some underwater objects will be reflected at the surface by total internal reflection-just as if the surface were a mirror-and mirror-images of them will appear above the water! Remember, we see something only by the light that actually reaches our eyes and then our eyes interpret that light assuming it has come along a straight path. Such a scuba diver is sketched in Figure 16.19. The figure looks rather messy-and there is a lot going on there-but let's look at the various pieces.
There is a bird flying directly above the scuba diver; light from
the bird strikes the surface normal to the surface (incidence
= 0) so it passes directly through without being bent. Light from
the bottom of the tree just skims the water's surface. When it
finally is bent, its angle of refraction is the critical angle,
49. The two heavier lines, in fact, mark the critical angle on
either side of the normal. Light from the top of the tree is bent
or refracted. The scuba diver sees these rays of light after they
have been refracted. So he then "sees" the tree-the
image of the tree, if you like-tilted and raised up toward the
center of his vision. Likewise, the cloud and sailboat are distorted;
their images are moved toward the normal. Everything above the
water's surface is seen inside a circle whose half-angle is the
critical angle (49 for air and water). Nothing that is seen outside
this circle originated above the water. But the view is not black
or void out there. Objects below the surface have their images
reflected in the surface as a mirror and appear there. This is
illustrated on both sides by the fish there.
Q: If light travels from glass into ethyl alcohol, will it be bent toward or away from the normal?
A: The index of refraction for glass is about 1.55
and the index of refraction for ethyl alcohol is 1.36. In going
from a material of higher index of refraction into a material
of lower index of refraction, light is bent away from the normal.
Q: If light travels from olive oil into air can the light undergo total internal reflection?
A: Total internal reflection can occur if the first index of refraction is greater than the second. Olive oil has an index of refraction of 1.47 which is greater than air's index of refraction of 1.0. Therefore, total internal reflection may occur.