Emerges parallel to initial ray
32.6 - Why refraction occurs
Why do waves change direction when they change speed? Here we offer a mechanical
analogy to explain this phenomenon.
Consider the diagram in Concept 1 to the right. It uses the example of a car
encountering ice on the side of a road. If this has ever happened to you, you know that
the car can dangerously change direction when one (or more) of its wheels encounters
ice, as shown in the diagram. Why is this so? The wheels on the ice provide less
traction, so the right side of the car moves more slowly. The left side of the car
continues to move at the same speed as before, which causes the car to rotate and
veer off the road. When all the wheels supplying power are on the ice, the car will once
again move straight ahead because both sides will be moving at the same speed.
Why light refracts can also be explained using Fermat’s principle of least time. This
principle, developed by French mathematician Pierre de Fermat (1601í1665), states
that light will travel the path between two points that requires the least amount of time.
This may seem like it should be a straight line, but it is not when the speed varies along
the path between two points.
This timesaving “technique” is similar to what you would intuitively do if you were standing on a beach and saw a swimmer floundering
desperately in the water some distance down the shore. Instead of taking a direct straight-line path to the rescue, you would run along the
beach for some distance, counting on your greater land speed, before taking to the water.
Car hits ice
Speed change on one side changes
direction of car32.7 - Interactive problem: helicopter and submarines
The simulation on the right is similar to the one in this chapter’s introduction. As
before, submarines lurk under the waves, but now you have only a single helicopter.
As before, you have a laser you can aim in an attempt to disable two submarines
before they disable you. You keep shooting as long as you keep making hits. To
shoot your laser, aim it by dragging the aiming arrow and fire it by clicking on FIRE.
The angle of incidence is shown in an output gauge.
As soon as you miss, it is the submarines’ turn. Warning: The computer has been
set to be far more accurate in this game than in the introductory one. Unless you are
very precise with your shots, it is unlikely you will win.
However, there is good news: Now you have more intellectual firepower because
you have the aid of Snell’s law. You are also given some assistance from an able
comrade; she has computed the angles of refraction required for your laser to reach
the submarines, as shown in the diagram. You should use 1.33 for the index of
refraction of water, and 1.00 for the index of refraction of air. If you correctly set the
angle of incidence when you aim each of your shots, you can make two straight hits
and disable the submarines before they disable you.
32.8 - Total internal reflection
Total internal reflection: Light reflects
completely at an interface, back into the
medium with the higher refractive index.
Critical angle: The minimum angle of incidence
at which total internal reflection occurs.
Total internal reflection means no light passes from one medium to another. On the
right, we show how this occurs using the example of an underwater flashlight shining a
beam at the interface between water and air. As the diagram shows, all the light reflects
back into the medium with the higher refractive index, the water. No light passes into
the air above the water.
Why does this occur? Consider what happens when light is directed from water into air.
Water has a greater index of refraction than air. At relatively small angles of incidence, light passes from the water into the air, and as it does
so, it refracts away from the normal. The angle of refraction is greater than the angle of incidence.
As the angle of incidence increases, the angle of refraction will increase as well, and it will always be greater than the angle of incidence. At a
Total internal reflection
No incident light leaves initial medium
Light is reflected at interface