# What is Snell's Law?

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• 0:04 The Law of Refraction…
• 2:40 Sample Problems
• 4:22 Calculating the Critical Angle
• 5:48 Lesson Summary

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Lesson Transcript
Instructor: Nissa Garcia

Nissa has a masters degree in chemistry and has taught high school science and college level chemistry.

What happens when light travels from one medium to another, like from air to water? The answer can be described by Snell's Law, which is the main focus of this lesson.

## The Law of Refraction and Snell's Law

Have you ever tried putting a pencil in a glass of water? Try it yourself, and if you look carefully from the surface of the water, you will see that the pencil will appear to be broken. This is because of a phenomenon called refraction.

So, what is refraction? When light travels through empty space, it normally travels in a straight line. However, when light travels from one medium to another, refraction takes place. Refraction is the bending of light when it travels from one medium to a different type of medium.

Let us compare ourselves to light - our speed is faster when we walk normally on the ground than when we try to walk through a swimming pool because water is a denser medium than air. The same thing can be said with the behavior of light - the speed at which it travels through air is faster than through a denser medium like water. Because of this, light becomes refracted or it bends.

When refraction occurs, the parts of the light-stream take on different names. In this illustration, the incident ray, which is the light that strikes the surface, first travels through the air. However, when it hits the surface of water, the light bends, or is refracted. This is called the refracted ray, which is the ray that enters the medium. The normal line is the line that is perpendicular to the surface. The angle of the incidence differs from the angle of refraction because of the change in the medium (from air to water).

Each medium has a different index of refraction, called n. The index of refraction measures the amount of bending of light. For instance, the index of refraction of air is n=1, and the index of refraction of water is n= 1.33, so light bends differently for each medium. Here is a table of a few different indices of refraction of different mediums.

Just like how we walk slower in a swimming pool, the speed of light behaves the same way. Light travels faster through air (n=1) than water (n=1.33) because water is denser than air. So, we can say that the higher the index of refraction, the denser the medium. Light travels slower in denser medium.

So, we can most definitely say that refraction is dependent on the medium through which light passes. This relationship is explained mathematically by Snell's Law. Snell's Law gives the equation which shows how light is refracted when it travels through two different mediums that have two different indices of refraction. The formula for Snell's Law is this:

## Sample Problems

How exactly can we use Snell's Law? Since Snell's Law involves refraction, the indices of refraction of different mediums, n, are always different for each medium. Let's go over a few different sample problems.

### Problem 1

Let's use the example of light passing through air and then through water, as shown again here:

Let's say we shine a light from air (n1=1) into water (n2=1.33). We know the angle of incidence (theta1), but we don't know the angle of refraction (theta2). We can use Snell's Law to find the angle of refraction (theta2).

Based on this example, when n1 is less than n2, the angle of incidence is greater than the angle of refraction. When light passes from less dense medium to denser medium, light bends towards the normal.

Now, let's try a second problem.

### Problem 2

Let us imagine light traveling from acetone (n1=1.36) to air (n2=1.33). The angle at which light travels through acetone is not known (theta1), and the angle at which light travels through air is 40 degrees (theta2). Here, we can use Snell's Law to find the angle of incidence (theta1).

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