# AP Physics 2 : Total Internal Reflection

## Example Questions

### Example Question #1 : Total Internal Reflection

A scuba diver is wearing a head lamp and looking up at the surface of the water. If the minimum angle to the vertical resulting in total internal reflection is , what is the index of refraction of the water?

Explanation:

We can use Snell's law:

At the first instance of total internal reflection, the angle of light on the air side will be  to the vertical, so the equation becomes:

Rearranging for the index of refraction of water, we get:

### Example Question #1 : Total Internal Reflection

A ray of light makes a transition from a sample of benzene to water. What is the minimum angle the light must make with respect the normal in order for the light to be completely reflected back into the sample of benzene?

The index of refraction for water is 1.33 and for benzene is 1.50.

Total internal reflection will not occur at any angle for the situation described

Explanation:

What this question is essentially asking for is the critical angle, which is the angle at which total internal reflection occurs. When this happens, the light will bend at an angle of  from the normal, or essentially along the interface of the two media. To solve for this value, we'll need to make use of Snell's law:

Where  is the index of refraction for benzene and  is the index of refraction for water.

To determine the critical angle, we'll make the following adjustments:

And plugging in values:

This is the angle where the incident light ray will be refracted at exactly . Any incident angle larger than this value will result in total internal reflection, where the light ray will essentially bounce back into the medium in which it originated.

Also, one very important thing to keep in mind is that total internal reflection can only occur when light travels from a medium with a higher index of refraction to a second medium with a lower index of refraction. So in the example given, total internal reflection can only occur when light travels from benzene (higher index) to water (lower index) and not the other way around.

### Example Question #1 : Total Internal Reflection

You have a piece of optical wire with a light beam traveling through it surrounded by a liquid with an index of refraction of 1.33. If the index of refraction of the wire is 1.85, what is the critical angle needed to achieve total internal reflection?

These materials cannot achieve total internal reflection.

Explanation:

The equation to find total internal reflection is a special case of Snell's Law, with the refraction angle set to . This new equation looks like this:

To find the critical angle, we can rearrange the equation.

As you can tell from this, the index of refraction of the medium the light is traveling from must be higher than the index of refraction of the other medium. Our numbers qualify. Now, we can plug in our values to find the critical angle.

### Example Question #4 : Total Internal Reflection

What is the critical angle for light traveling from glass to water? Glass has an index of refraction of , while water has .

Explanation:

To find the critical angle in total internal reflection problems, the following equation must be used:

where the subscripts  stands for critical,  stands for refraction, and  stands for incident index of refraction.

Plug in the values and solve for the critical angle:

Here, the incident index of refraction belongs to water.

### Example Question #81 : Optics

Suppose that a ray of light passes from a medium with an index of refraction of  into another medium with an index of refraction of . If the incident ray is at an angle of  with respect to the normal, what is the critical angle?

There is no critical angle in this scenario