# AP Physics 2 : Snell's Law

## Example Questions

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### Example Question #1 : Snell's Law

A ray of light is traveling through air at an angle of  to the vertical. It passes into water and halves its angle to the vertical. What is the index of refraction of water?

Explanation:

This problem can be solved using Snell's law:

Rearrange to solve for for the index of refraction of water

We can determine the second angle:

We have all the values for Snell's law, allowing us to solve:

### Example Question #2 : Snell's Law

A beam of light going through a medium with an index of refraction of 1.14 has an angle of incidence of  with another medium. If the light wave is at a new angle of , what is the index of refraction for the second medium?

There is not enough information to determine the index of refraction.

Explanation:

To find the index of refraction, we use Snell's Law:

We have values for , , and , so now we just need to rearrange the equation to solve for .

Now, we can just plug in our numbers.

Therefore, the index of refraction of the second material is 1.346.

### Example Question #3 : Snell's Law

Find the angle of refraction if a light beam enters water at an angle of  relative to the normal.

and

Explanation:

To find the angle of refraction, use the Snell's law equation to determine the angle.

Find the index of refraction for water.

Find the index of refraction for air.

Solve for .

### Example Question #4 : Snell's Law

A cup of water sitting on a table outside in the sunlight is filled to the top. The sun happens to be  above the horizon and you notice the bottom of the cup has just become completely shaded. The cup has a depth of  and you realize you can calculate the width of the bottom of the cup.  Find the width in .

Explanation:

This problem is a Snell's Law problem. There is some information not stated but can be found in your text book such as the index of refraction of water. A picture will help us see what is going on in this problem,

will be defined as the angle w.r.t. the horizon that the sun is at. Let  be the depth of the water and since the light passes through air  into water , it is just an application of Snell's Law, then a simple trig calculation.

First, let's find ,

Now apply Snell's Law to find ,

Now there is a right triangle with sides  and  and an angle of . Using the tangent,

### Example Question #5 : Snell's Law

A ray of light initially travelling through the air enters a material at a angle of  with respect to the line normal to the surface. The light is this observed to bend toward the normal by . Calculate the index of refraction ,, of the material.

Explanation:

By Snell's law, we have the relation between the incident angle , the refracted angle , and the indices of refraction of the two materials  and  given by:

The index of refraction of air is taken to be . By substituting in the given values into our rearranged equation, we can solve for the index of refraction of the material.

### Example Question #6 : Snell's Law

A laser initially moving through air enters a medium that has an index of refraction . The beam's angle with respect to the normal inside the material is measured to be . Calculate the incident angle (the angle the laser made with respect to the normal before entering the material).

Explanation:

Using Snell's Law, we can use the information given to solve for . This is shown below as:

Solve for the incident angle.

Plug in and solve:

### Example Question #7 : Snell's Law

Suppose that a ray of light traveling through air strikes the surface of a body of water, and the ray of light then begins traveling through the water. If the ray of light from air hits the surface of the water at an angle of  from the horizontal, then how far from the horizontal will the ray of light in water be bent?

Explanation:

This question is presenting us with a scenario in which light is first traveling through air, and then it hits the surface of water and begins traveling through the water. We're provided with the angle of the incident light, and are asked to find the angle of the light with respect to the horizontal after refraction has occurred.

To answer this question, we'll need to make use of Snell's law:

Where  and  represent the index of refraction for air and water, respectively. Furthermore,  is the angle of the incident light ray (from air) with respect to the normal, while  is the angle of the refracted ray in water with respect to the normal.

When establishing the values for the variables listed above, it's important to be aware of the difference between the angle with respect to the horizontal (as presented in the question stem) and the angle with respect to the normal (which is perpendicular to the surface boundary). In the question stem, we're told that the incident light ray strikes the surface boundary at an angle of  with respect to the horizontal. This means that the angle with respect to the normal will be .

Now, we have all the information we need to solve for the missing angle. But first, we can rearrange the above equation to isolate the variable we're looking for.

But there's one more very important thing we have to do. Recall that the question is asking for the resulting angle with respect to the horizontal, whereas this answer is telling us the angle with respect to the normal. Therefore, we will need to convert this angle:

### Example Question #8 : Snell's Law

Light travels from air to water . If the angle of incidence is , determine the angle of refraction.

None of these

Explanation:

Snell's Law:

Where

is the respective incident angle

is the respective velocity of the light

is the respective wavelength

is the respective index of refraction

Use Snell's Law

Solve for :

Plug in values:

Solving:

### Example Question #9 : Snell's Law

Light travels from air to water . If the angle of incidence is , determine the angle of refraction.

None of these

Explanation:

Snell's Law:

Where

is the respective incident angle

is the respective velocity of the light

is the respective wavelength

is the respective index of refraction

Use Snell's Law

Solve for :

Plug in values:

Solve:

### Example Question #10 : Snell's Law

Light travels from air to water . If the angle of incidence is , determine the angle of refraction.

None of these

Explanation:

Snell's Law:

Where

is the respective incident angle

is the respective velocity of the light

is the respective wavelength

is the respective index of refraction

Use Snell's Law

Solve for :

Plug in values:

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