Refraction pics

Pictures and text by Damien Martin

What is refraction?
Refraction in the real world.
What is total internal reflection?
Total internal reflection pictures.
All images

What is refraction?

Here are a collection of pictures demonstrating refraction &ndash the bending of light as it goes from one medium to another. The examples are all from a swimming pool and air, in which the water is the "slow" medium (n_water=1.33) and air is the "fast" medium (n_air = 1.0).

When going from a slower to a faster medium, light bends away from the normal. When going from a faster to a slower medium, light bends toward the normal. The pictures below illustrate exactly what is meant by these statements.

When going from a slower to a faster medium, light bends away from the normal. When going from a faster to a slower medium, light bends toward the normal.

Mathematically, we can calculate the angle in either medium, provided we know the indicies of refraction (called n_air, n_water, ..., n_medium) and the angle in the other medium by using Snell's law:

n_air sin &theta_air = n_water sin &theta_water A picture showing the meaning of these angles is shown below:

Refraction in the real world

Here we start with a straight rod used for cleaning pools (click to enlarge):

By placing this rod into the swimming pool, we see that it appears to bend. This is refraction at work! See if you can figure out or explain using the rules above why it bends the way it does. (Click either figure to enlarge)

What is total internal reflection?

A trick

Take a look at the picture shown below:

It looks like a moon setting over a body of water, with the moon's reflection in the surface. We can even see floating leaves on the water's surface.

That is not what this picture is. This picture is upside-down &ndash instead we are looking at a light in the swimming pool, and the light's reflection on the surface of the water. The picture the right way up is shown below:

This is an example of total internal reflection.

Why do we get total internal reflection?

We have learned that when light goes from a slow medium to a fast medium that the light bends away from the normal. But we can make the angle in the slow medium as close to 90 degrees as we like -- which means that eventually we will "run out of room" to bend the light! The series of images below illustrate this point:

Where does the light go after we no longer have any more room in the air for it to bend into? The answer is that it is all reflected. Of course, in all these pictures some light is reflected but we have only drawn the refracted ray. A more realistic series of diagrams is shown below, with thicker lines corresponding to brighter light:

Only in the last picture do we get total internal reflection.

Moon off the water

Total internal reflection never occurs when light goes from a fast medium to a slow medium. That is because there is always enough room to bend toward the normal.

But what about the moon reflecting off the surface of the water? It turns out that while we do get a strong reflection, the moon light also gets transferred into the water – it is a strong reflection but some is still transmitted. While the difference would be noticable from the point of view from someone in the water, it is difficult to tell the difference from the point of view of someone in the air.

Real total internal reflection

Here are pictures taken from the swimming pool that show total internal reflection and illustrate where the critical angle is between air and water.

Simple reflections in the surface

These pictures are all taken under water.

These pictures show both my foot in the water and a reflection of my foot in the surface of the water. The ripples on the surface of the water change the normal slightly, hence the distorsion of the image.

Here are a couple of pictures of someone's hand in the water. The picture on the left is at an angle close to the normal, therefore there is almost no reflection and we can see the hand. On the right the picture is taken far from the normal and total internal reflection occurs. Looking at the larger version we can see the image of the drain on the bottom of the pool in the upper right hand corner (the drain can be seen on the lower left had corner). Click on either image to enlarge.

Critical angle

These pictures show the critical angle. These pictures show the transition from refraction (where we can see through the surface of the water) and total internal reflection.

This last picture shows a good example of reflection from the surface of the water that is not total internal reflection. We can see the partial reflection of the wrist and arm, as well as total internal reflection of the hand.

Finding the critical angle mathematically

To actually find the critical angle mathematically, we solve for θ_air: sin θ_air = (n_water/n_air) sin θ_water Because n_water > n_air the right-hand side can be greater than one. The left hand side is the sine of an angle, and therefore can be at most one. These sides cannot be equal for all angles, and total internal reflection occurs for those angles for which Snell's law fails.

Setting the LHS to one (the largest it can be) we can find the largest θ_water possible. Any greater angle will give total internal reflection. i.e.

sin θ_{water, crit} = (n_air/n_water) = 0.75 Taking the inverse sine tells us θ_{water, crit} = 48.6 degrees.

(This argument can also be used to show that total internal reflection cannot occur when light goes from a fast medium to a slow medium.)

All images

Here are all the images taken from the pool that show something interesting about optics. Physics is all around us!


When going from a slower to a faster medium, light bends away from the normal.	When going from a faster to a slower medium, light bends toward the normal.