# Refraction

We have all seen things that are due to the concept that physicists call Refraction. For example, when a straw is placed in a glass of water, the straw appears to be bent. This is illustrated on the right.

What happens if we send a beam of laser light into an aquarium?

In general, we can see the path that the laser beam took inside the water, because the light reflects off of impurities in the water. The end result, as shown below, is a laser that is disconnected from the "beam" inside the water.

It is important that we differentiate seeing where the light went from seeing it go there. The speed of light is incredibly fast, so we can't really see it move from point to point. We are allowed to see where it went, however, as part of the beam reflects off of small particles of dust, etc. in the water. Separate the light beam from the path it takes in your mind.

Why can't we see the path the laser beam took though the air above the aquarium? The answer is simply that there are no small particles in the air to reflect the light towards our eyes.

How can we see the beam in air, then? How about putting some small particles in the air for the light to scatter from!

If we put some smoke in the space above the water, or some chalk dust, or even the mist from a spray bottle, part of the laser light can reflect off of the particles towards our eyes. When we do this, we see something like the diagram above.

From the diagram we see that light bends going from air into the water. This bending is called Refraction.

What happens if we change the angle that light strikes the surface? In this case, the angle inside the water changes, too. A series of different directions is shown here. Is there any regularity to the pattern?

Physicists add a new line to the situation called a normal. In the diagram below, notice that the normal is simply a line perpendicular to the surface at the point where the light enters the water.

We use the angle formed between the light in air and the normal, which they would call the incident angle. They also use the angle between the light in water and the normal, which is called the refracted angle.

Which of the angles is larger? Does it matter how large the incident angle was to begin with?

What conclusions do we reach about the general trend for light entering water from air?

We say that light bends so that it is closer to the normal when it moves from air into water. In our example, this means that the Refracted Angle is smaller than the Incident Angle.

What happens if light goes from water into the air? We imagine a mirror placed on the bottom of the aquarium, reflecting the laser light back upwards towards the surface. As we check things out, the pattern followed resembles the one below: It looks like the pattern upon entering water is just reversed when light leaves water.

Indeed! If light bends closer to the normal upon entering water, it bends further from the normal upon leaving it. This is a nice example of the "reversibility" of many light phenomena.

At this point we carry out careful experiments to determine the amount of bending that light undergoes while travelling from air to water. As we do, a mathematical pattern emerges.

We label the respective angles as in the diagram. It turns out that the ratio, not of the angles, but of their sines forms a constant:

This important rule about the behavior of light is called Snell's Law, but we haven't seen it in its most general sense. We've only seen it for air and water. In order to get a more general rule, we must do more experimentation.

As a result of more work, we end up defining a new term, the index of refraction, n, for each substance. In practice, n has a value of 1.00 or greater. Some typical values for the index of refraction are given here:

 Substance n Air 1.00 Water 1.33 Glass 1.50± Plastic 1.40± Diamond 2.42

Our new picture of refraction has light going from one substance, identified with the subscript 1, into a second substance, subscript 2. We also identify the angles relative to the normal with the same subscripts.

The full form of Snell's Law is written as below:

Now if the new medium has a higher index of refraction, the corresponding sine of the angle must decrease. In order for this to happen, the angle must decrease.

In the diagram above right, medium 1 has a lower index of refraction, while medium 2 has the higher value. Note the relative angle sizes for q1 and q2 .

### PARALLEL SIDES:

What happens to the path of light going through a transparent medium like plastic or glass which has parallel sides? The general pattern is shown here with angles designated a q1 , q2, q3 and q4. The index of refraction of the parallel-sided object is n2.

At each of the changes of medium, light bends and Snell's Law applies. Thus we have two equations:

n1 sin q1 = n2 sin q2

n2 sin q3 = n1 sin q4

But the second and third angles (q2 and q3) can be shown to be equal since the normals are parallel and they are alternate interior angles. Therefore the second and third terms are equal which makes the first and last terms equal. The bottom line is the angle formed with the normal on exiting the object is exactly the same as the angle formed on entering it.

n1 sin q1 = n2 sin q2 = n2 sin q3 = n1 sin q4

n1 sin q1 = n1 sin q4

q1 = q4

Note that this result is only true if the sides are parallel.

### BOX OF AIR:

What happens if the rectangular box is not at a higher index of refraction than the surrounding medium? Such would be the case if an empty plastic box were submerged in water. Apply Snell's Law just as before, but note that the angle inside the box is larger than the angle outside:

In this case the emerging ray will be parallel to the incoming ray just as before. But notice that it has been shifted sideways in a different manner. It is important to apply Snell's Law and logic consistently and to allow the problem to dictate which is n1, n2, etc.

### AQUARIUM:

Does an object behind an aquarium appear to be located at its real position? In your lab work you traced the shadows (or light by extension) coming from a source behind the plastic block "aquarium". A possible scenario is shown here:

If we are at the bottom looking up towards the object, the light rays that would actually get to us are the ones shown emerging from the aquarium. So in our mind we trace them back to where they appear to have originated as shown below with the dotted lines.

Thus the object appears to be located at a position that is closer than it really is. The light going through the aquarium has changed direction twice with the end result of altering the apparent location of objects. It is left to you to use similar reasoning to determine the apparent location for objects that are inside the aquarium but observed from outside.

Future additions will go into problem solving with Snell's Law.

There is a related topic called Total Internal Reflection. Click on the link below to go to that section or click on the Back button to return to the main menu.