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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.

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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.

Light is Refracted When it Travels From One Medium to Another Medium
Refraction


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.

Table of Indices of Refraction of Different Mediums
Indices of Refraction


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:

Snell


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).

Snell


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).


Snell


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

Calculating the Critical Angle Using Snell’s Law

We can also use Snell’s Law to calculate the critical angle. When light travels from a denser medium to a less dense medium (or when n1 is greater than n2), in order for refraction to occur, the angle of incidence needs to be lower than a certain value. This is what we call the critical angle.The critical angle is the value of the angle of incidence (theta1) when the angle of refraction is equal to 90 degrees (theta2).

The critical angle can be calculated using Snell’s Law, as shown here:

How to Find the Critical Angle
Critical Angle


This illustration shows how light travels when the angle of refraction is 90 degrees. Here, light passes from water to air, so n1 is greater than n2. When the angle of refraction is 90 degrees, the angle of incidence is equal to the critical angle (thetaC).


The angle of incidence = critical angle when the angle of refraction is 90 degrees
Critical Angle picture


What is the significance of finding the critical angle? This tells us that the angle of incidence should be lower than the critical angle for refraction to occur. What if it is higher? If the angle of incidence is greater than the critical angle, then refraction does not occur.Let us try calculating the critical angle for when light passes from water to air:

Critical Angle For Air-Water Boundary
This means that in order for refraction to occur, the angle of incidence should be less than 48.5 degrees.

Lesson Summary

Refraction occurs when light bends while passing from one medium to another. Snell’s Law shows the mathematical relationship between the angles of incidence and refraction of light when passing through two different mediums with different indices of refraction. The values of an index of refraction reflects how dense a medium is – the higher the index of refraction, the denser the medium. When the medium is denser, then light travels more slowly through it.Based on the problems we solved earlier, here are a couple of things we also need to remember:

  • When light travels from a less dense to a denser medium, light bends towards the normal, so the angle of incidence is greater than the angle of refraction.

  • When light travels from less dense to a denser medium, the speed of light decreases.

We can also use Snell’s Law to calculate the critical angle, which is the value of the angle of incidence when the angle of refraction is equal to 90 degrees (or perpendicular to the normal line). If the angle of incidence exceeds the critical angle, then refraction will not occur.

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