Refraction and Snell's law | Geometric optics | Physics | Khan Academy

Summary

This video script delves into the concept of light refraction, where light changes direction as it passes from one medium to another. It explains the phenomenon using the analogy of a car transitioning from a road to mud, illustrating how the change in speed causes a change in direction. The script introduces Snell's Law, which quantifies the relationship between the angles of incidence and refraction, and the velocities of light in different media. It also discusses the index of refraction, providing examples of its values for various materials, to offer an intuitive understanding of how light behaves when it encounters different environments.

Takeaways

• 🌟 Reflection is the process where light bounces off a surface, with the incident angle equaling the reflected angle, measured relative to a perpendicular.
• 🔄 Refraction occurs when light passes from one medium to another, changing its speed and direction, causing the light to bend.
• 🚀 Light travels fastest in a vacuum, with no medium to impede its speed.
• 💧 The script uses the example of light traveling from a vacuum into water to explain refraction, despite it being an unlikely natural scenario.
• 🚗 An analogy is made comparing light refraction to a car transitioning from a road to mud, where the wheels on one side slow down first, causing the car to turn.
• 📐 Snell's Law is introduced as the mathematical relationship between the angles of incidence and refraction and the velocities of light in the two media.
• 🔢 The index of refraction (n) is defined as the speed of light in a vacuum divided by the speed of light in a medium, indicating how much light slows down in different materials.
• 🔄 Snell's Law can be expressed in terms of the index of refraction, showing the ratio of the sine of the angles to the indices of refraction on either side of the interface.
• 📉 A higher index of refraction indicates that light travels slower in that medium compared to a vacuum.
• 📈 The script provides a list of refraction indices for various materials, highlighting that the index is 1 for a vacuum and varies for other materials like air and diamond.
• 🔍 The next video is teased to further explore Snell's Law with examples, including the visual illusion of a bent straw due to refraction.

Q & A

What is the basic concept of reflection as discussed in the script?

Reflection is the idea of light rays bouncing off a surface. When the surface is smooth, the incident angle is equal to the reflected angle, and these angles are measured relative to a perpendicular.

What phenomenon occurs when light passes from one medium to another?

When light passes from one medium to another, the phenomenon of refraction occurs, where the light changes direction and bends as it enters a medium with a different optical density.

What is Snell's Law and how does it relate to refraction?

Snell's Law relates the angles of incidence and refraction to the velocities of light in the two media. It states that the ratio of the sine of the angle of refraction to the sine of the angle of incidence is equal to the ratio of the velocities of light in the two media.

How does the script use the analogy of a car to explain refraction?

The script uses the car analogy to illustrate how light bends when it moves from a faster medium to a slower one. It compares the light to a car that turns when its wheels on one side slow down due to a change in the surface, similar to how light bends when it enters a denser medium.

What is the speed of light in a vacuum and how is it represented?

The speed of light in a vacuum is the fastest speed at which light can travel, represented by 'c', and it is approximately 300 million meters per second or 300,000 kilometers per second.

What is the index of refraction and how is it defined?

The index of refraction, represented by 'n', is a measure of how light propagates through a particular medium. It is defined as the speed of light in a vacuum (c) divided by the velocity of light in that medium.

How does the script explain the concept of the angle of incidence and angle of refraction?

The angle of incidence (theta 1) is the angle at which the light ray strikes the interface between two media. The angle of refraction (theta 2) is the angle at which the light ray bends after entering the new medium. Both angles are measured relative to a perpendicular line to the interface.

What is the significance of the refraction index in Snell's Law?

The refraction index in Snell's Law is used to express the ratio of the speed of light in a vacuum to the speed of light in a given medium. It simplifies the law by using a single value that represents the optical density of the medium.

How does the script describe the relationship between the speed of light and the refraction index?

The script describes that in a medium where light travels slower, the refraction index is larger because it is the ratio of the maximum speed of light (in a vacuum) to the actual speed of light in that medium.

What are the practical implications of understanding refraction and Snell's Law?

Understanding refraction and Snell's Law is crucial in various fields such as optics, where it helps in designing lenses and understanding how light interacts with different materials. It also helps explain everyday phenomena like why a straw appears bent in a glass of water.

How does the script suggest visualizing Snell's Law with the refraction indices of different materials?

The script suggests using Snell's Law in the form that involves refraction indices to visualize and understand why light bends when moving from one medium to another, by comparing the refraction indices of the two media involved.

Outlines

00:00

🌟 Introduction to Refraction and Light Behavior

This paragraph introduces the concept of refraction, where light changes direction as it passes from one medium to another, unlike reflection where light bounces off a surface. It explains the scenario of light traveling from a vacuum (fastest speed) to water (slower speed), causing the light to bend towards the normal due to the change in medium. The paragraph uses an analogy of a car transitioning from a road to mud to help visualize why the light bends, emphasizing the intuitive understanding of refraction without delving into the complex physics of light.

05:02

🚗 Analogous Explanation of Refraction Using a Car

Building upon the initial explanation, this paragraph uses the car analogy to further clarify the concept of refraction. It describes how a car's wheels would behave differently when transitioning from a road to a slower medium like mud, causing the car to turn. This serves as a metaphor for how light 'turns' or bends when it moves from a faster medium to a slower one, such as from air to glass. The paragraph also introduces Snell's Law as the mathematical relationship governing the angles of incidence and refraction.

10:02

🔍 Deep Dive into Snell's Law and Refraction Indices

This paragraph delves deeper into Snell's Law, providing a mathematical framework for understanding refraction. It explains the relationship between the velocities of light in different media and how these relate to the sine of the angles of incidence and refraction. The paragraph introduces the concept of the index of refraction, denoted by 'n', which is the ratio of the speed of light in a vacuum to its speed in a given medium. It also reformulates Snell's Law using the index of refraction, illustrating how the product of the index and the sine of the refraction angle equals the product of the same for the incidence angle, offering a clearer perspective on how different media affect the path of light.

Keywords

💡Reflection

Reflection refers to the phenomenon where light rays bounce off a surface. In the context of the video, it is a crucial concept that sets the stage for understanding refraction. The script explains that if the surface is smooth, the angle of incidence is equal to the angle of reflection, both measured relative to a perpendicular line to the surface. This concept is foundational to the study of optics and is essential for grasping how light behaves when it interacts with different surfaces.

💡Refraction

Refraction is the bending of light as it passes from one medium to another with a different refractive index. The video script describes refraction by illustrating how light changes direction when moving from a vacuum into water or glass, which are slower media for light. Refraction is central to the video's theme, as it explains how the change in the speed of light causes it to bend, a concept that is explored in detail through the analogy of a car transitioning from a road to mud.

💡Incident Angle

The incident angle, often denoted as theta 1 in the script, is the angle at which light strikes the boundary between two different media. It is a fundamental aspect of both reflection and refraction, as it determines how light will behave upon encountering a new medium. The script uses this term to describe the initial angle of the light ray before it interacts with the second medium, which is critical for understanding the subsequent bending of light due to refraction.

💡Refraction Angle

The refraction angle, symbolized as theta 2 in the script, is the angle that the refracted light ray makes with the normal (perpendicular) to the surface after passing into a new medium. It is a direct result of refraction and is used in the script to describe the direction of the light after it has entered a medium where it travels slower, such as water or glass.

💡Snell's Law

Snell's Law is a formula that relates the angles of incidence and refraction to the refractive indices of the two media involved. The script explains Snell's Law as the ratio of the velocities of light in the two media to the sines of the respective angles. This law is central to the video's educational message, as it provides the mathematical framework for understanding and calculating the behavior of light at the interface between different media.

💡Index of Refraction

The index of refraction, denoted as 'n' in the script, is a measure of how much slower light travels in a given medium compared to a vacuum. It is defined as the speed of light in a vacuum divided by the speed of light in the medium. The script uses the index of refraction to rewrite Snell's Law in a more intuitive form, showing how it affects the bending of light and is a key concept for understanding the differences in how light behaves in various materials.

💡Normal

The normal is an imaginary line perpendicular to the surface at the point where the light ray strikes. In the script, the normal is used as a reference for measuring the incident and refraction angles. It is essential for understanding how the angles are defined and how they relate to the behavior of light during reflection and refraction.

💡Vacuum

A vacuum, as described in the script, is a space devoid of matter, including air and water. It is the medium in which light travels at its fastest speed. The script uses the vacuum as a reference point to compare the speed of light in other media, such as water or glass, to illustrate the concept of refraction.

💡Medium

In the context of the script, a medium is any material through which light travels. Different media have different refractive indices, affecting the speed and direction of light. The video discusses how light behaves when it moves from one medium, like a vacuum, to another, such as water or glass, which is fundamental to understanding refraction.

💡Analogy

An analogy is a comparison between two different things to explain a concept or principle. The script uses the analogy of a car transitioning from a road to mud to help viewers intuitively understand why and how light bends when it enters a slower medium. This analogy is a key part of the video's narrative, making the abstract concept of refraction more tangible and relatable.

💡Optics

Optics is the branch of physics that studies the behavior and properties of light, including its reflection, refraction, and propagation. The script delves into various concepts of optics, such as reflection, refraction, Snell's Law, and the index of refraction, to provide a comprehensive understanding of how light interacts with different surfaces and media.

Highlights

Reflection is explained as the bouncing of light rays off a smooth surface with the incident angle equal to the reflected angle.

Introduction to refraction where light changes direction when passing from one medium to another.

Refraction involves light bending as it enters a medium where it travels slower, such as water from a vacuum.

The concept of Snell's Law is introduced as the mathematical relationship between the angles of incidence and refraction.

An analogy of a car transitioning from a road to mud to explain the intuitive concept of refraction.

The car analogy demonstrates how the wheels on one side of the car slow down first, causing the car to turn.

Light bends towards the normal when entering a slower medium, similar to the car turning towards the slower wheels.

Snell's Law is presented in terms of the ratio of velocities of light in two different media.

The index of refraction is defined as the speed of light in a vacuum divided by the speed of light in a medium.

Rewriting Snell's Law using the index of refraction instead of velocities provides an alternative perspective.

The refraction index varies for different materials, affecting how much light bends when it enters them.

The vacuum has an index of refraction of 1, as it is the medium where light travels at its fastest speed.

Air has a close to 1 index of refraction, indicating light travels nearly as fast as in a vacuum.

Diamond has a higher index of refraction, meaning light travels significantly slower in diamond than in a vacuum.

Upcoming videos will apply Snell's Law with examples, including the visual illusion of a bent straw.

The transcript aims to ensure a basic understanding of refraction before delving into further applications.

Transcripts

In the last couple of videos we talked about reflection.

And that's just the idea of the light rays bouncing off of a surface.

And if the surface is smooth, the incident angle is going to be the same thing as the reflected angle.

We saw that before, and those angles are measured relative to a perpendicular.

So that angle right there is going to be the same as that angle right there.

That's essentially what we learned the last couple of videos.

What we want to cover in this video is

when the light actually doesn't just bounce off of a surface

but starts going through a different medium.

So in this situation, we will be dealing with refraction.

Refraction. Refraction, you still have the light coming in to the interface between the two surfaces.

So let's say--so that's the perpendicular right there,

actually let me continue the perpendicular all the way down like that.

And let's say we have the incident light ray coming in at some, at some angle theta 1,

just like that...what will happen--and so let's say that this up here, this is a vacuum.

Light travels the fastest in a vacuum.

In a vacuum. There's nothing there, no air, no water, no nothing, that's where the light travels the fastest.

And let's say that this medium down here, I don't know, let's say it's water.

Let's say that this is water.

All of this. This was all water over here.

This was all vacuum right up here.

So what will happen, and actually, that's kind of an unrealistic--

well, just for the sake of argument, let's say we have water going right up against a vacuum.

This isn't something you would normally just see in nature

but let's just think about it a little bit.

Normally, the water, since there's no pressure, it would evaporate and all the rest.

But for the sake of argument, let's just say that this is a medium where light will travel slower.

What you're going to have is

is this ray is actually going to switch direction, it's actually going to bend.

Instead of continuing to go in that same direction, it's going to bend a little bit.

It's going to go down, in that direction

just like that. And this angle right here, theta 2,

is the refraction. That's the refraction angle. Refraction angle.

Or angle of refraction. This is the incident angle, or angle of incidence,

and this is the refraction angle. Once again, against that perpendicular.

And before I give you the actual equation of how these two things relate

and how they're related to the speed of light in these two media--

and just remember, once again, you're never going to have vacuum against water,

the water would evaporate because there's no pressure on it and all of that type of thing.

But just to--before I go into the math of actually how to figure out these angles

relative to the velocities of light in the different media

I want to give you an intuitive understanding of

not why it bends, 'cause I'm not telling you actually how light works

this is really more of an observed property

and light, as we'll learn, as we do more and more videos about it,

can get pretty confusing.

Sometimes you want to treat it as a ray, sometimes you want to treat it as a wave,

sometimes you want to treat it as a photon.

But when you think about refraction

I actually like to think of it as kind of a, as a bit of a vehicle,

and to imagine that, let's imagine that I had a car.

So let me draw a car. So we're looking at the top of a car.

So this is the passenger compartment, and it has four wheels on the car.

We're looking at it from above.

And let's say it's traveling on a road.

It's traveling on a road. On a road, the tires can get good traction.

The car can move pretty efficiently, and it's about to reach an interface

it's about to reach an interface where the road ends and it will have to travel

on mud. It will have to travel on mud. Now on mud, obviously, the tires' traction

will not be as good. The car will not be able to travel as fast. So what's going to happen?

Assuming that the car, the steering wheel isn't telling it to turn or anything,

the car would just go straight in this direction.

But what happens right when--which wheels are going to reach

the mud first? Well, this wheel. This wheel is going to reach the mud first.

So what's going to happen? There's going to be some point in time

where the car is right over here. Where it's right over here.

Where these wheels are still on the road, this wheel is in the mud,

and that wheel is about to reach the mud.

Now in this situation, what would the car do?

What would the car do? And assuming the engine is revving and the wheels are turning,

at the exact same speed the entire time of the simulation.

Well all of a sudden, as soon as this wheel hits the medium, it's going to slow down.

This is going to slow down. But these guys are still on the road.

So they're still going to be faster.

So the right side of the car is going to move faster than the left side of the car.

So what's going to happen?

You see this all the time. If the right side of you is moving faster than the left side of you,

you're going to turn, and that's exactly what's going to happen to the car.

The car is going to turn. It's going to turn in that direction.

And so once it gets to the medium, it will now travel, it will now turn--

from the point of the view from the car it's turning to the right.

But it will now travel in this direction. It will be turned when it gets to that interface.

Now obviously light doesn't have wheels, and it doesn't deal with mud.

But it's the same general idea. When I'm traveling from a faster medium

to a slower medium, you can kind of imagine the wheels on that light

on this side of it, closer to the vertical, hit the medium first, slow down,

so light turns to the right.

If you were going the other way, if I had light coming out of the slow medium,

so let's imagine it this way. Let's have light coming out of the slow medium.

And if we use the car analogy, in this situation, the left side of the car is going to--

so if the car is right over here, the left side of the car is going to come out first

so it's going to move faster now. So the car is going to turn to the right, just like that.

So hopefully, hopefully this gives you a gut sense of just how to figure out which direction

the light's going to bend if you just wanted an intuitive sense.

And to get to the next level, there's actually something called Snell's Law.

Snell's Law.

Snell's Law. And all this is saying is that this angle--

so let me write it down here--so let's say that this velocity right here is velocity 2

this velocity up here was velocity 1, going back to the original.

Actually, let me draw another diagram, just to clean it up.

And also that vacuum-water interface example, I'm not enjoying it,

just because it's a very unnatural interface to actually have in nature.

So maybe it's vacuum and glass. That's something that actually would exist.

So let's say we're doing that. So this isn't water, this is glass. Let me redraw it.

And I'll draw the angles bigger.

So let me draw a perpendicular.

And so I have our incident ray,

so in the vacuum

it's traveling at v1--and in the case of a vacuum,

it's actually going at the speed of light, or the speed of light in a vacuum,

which is c, or 300,000 kilometers per second,

or 300 million meters per second--let me write that--

so c is the speed of light in a vacuum,

and that is equal to 300--

it's not exactly 300, I'm not going into significant digits--

this is true to three significant digits--300 million meters per second.

This is light in a vacuum.

Light in vacuum. And I don't mean the thing that you use to clean your carpet with,

I mean an area of space that has nothing in it.

No air, no gas, no molecules, nothing in it. That is a pure vacuum

and that's how fast light will travel.

Now it's travelling really fast there, and let's say that--and this applies to any two mediums--

but let's say it gets to glass here, and in glass it travels slower,

and we know for our example, this side of the car

is going to get to the slower medium first

so it's going to turn in this direction.

So it's going to go like this.

We call this v2.

Maybe I'll draw it--if you wanted to view these as

vectors, maybe I should draw it as a smaller vector

v2, just like that.

And the angle of incidence is theta 1.

And the angle of refraction is theta 2.

And Snell's Law just tells us

the ratio between v2 and the sin--

remember Soh Cah Toa, basic trig function--

and the sin of the angle of refraction

is going to be equal to the ratio of v1 and

the angle--the sin of the angle of incidence.

Sin of theta 1.

Now if this looks confusing at all, we're going to

apply it a bunch in the next couple of videos.

But I want to show you also that

there's many many ways to view Snell's Law.

You may or may not be familiar with the idea of

an index of refraction.

So let me write that down.

Index of refraction.

Index, or refraction index.

And it's defined for any medium, for any material.

There's an index of refraction for vacuum, for air,

for water.

For any material that people have measured it for.

And they usually specify it as n.

And it is defined as the speed of light in a vacuum

That's c. Divided by the velocity of light in that medium.

So in our example right here, we could rewrite this.

We could rewrite this in terms of index of refraction.

Let me do that actually. Just cause that's sometimes

the more typical way of viewing Snell's Law.

So I could solve for v here if I--one thing I could do

is just--if n is equal to c divided by v

then v is going to be equal to c divided by n.

And I can multiply both sides by v

if you don't see how I got there.

The intermediary step is, multiply both sides times v,

you get v times n is equal to c, and then

you divide both sides by n, you get

v is equal to c over n.

So I can rewrite Snell's Law over here as

instead of having v2 there, I could write

instead of writing v2 there I could write

the speed of light divided by the refraction index

for this material right here.

So I'll call that n2.

Right, this is material 2, material 2 right over there.

Right, that's the same thing as

v2 over the sin of theta 2

is equal to v1 is the same thing as c divided by n1

over sin of theta 1. And then we could do a little bit

of simplification here, we can multiple both sides of

this equation--well, let's do a couple of things. Let's--

Actually, the simplest thing to do is actually

take the reciprocal of both sides.

So let me just do that.

So let me take the reciprocal of both sides,

and you get sin of theta 2 over cn2 is equal to

sin of theta 1 over c over n1.

And now let's multiply the numerator and

denominator of this left side by n2.

So if we multiply n2 over n2.

We're not changing it,

this is really just going to be 1,

but this guy and this guy are going to cancel out.

And let's do the same thing over here,

multiply the numerator and the denominator

by n1, so n1 over n1.

That guy, that guy, and that guy

are going to cancel out.

And so we get n2 sin of theta 2 over c is equal to

n1 sin of theta 1 over c.

And now we can just multiply both sides

of this equation by c and we get the form of

Snell's Law that some books will show you,

which is the refraction index for the slower medium,

or for the second medium, the one that we're entering,

times the index of the sin of the index of refraction

is equal to

the refraction index for the first medium

times the sin of the angle of incidence.

The incident angle.

So this is another version right here

This is another version right there of Snell's Law.

Let me copy and paste that.

And if this is confusing to you,

and I'm guessing that it might be,

especially if this is the first time you're seeing it,

we're going to apply this in a bunch of videos,

in the next few videos, but I really just want to make sure,

I really just want to make sure you're comfortable with it.

So these are both equivalent forms of Snell's Law.

One deals with the velocities, directly deals with

the velocities, right over here,

the ratio of the velocity to the sin of the incident

or refraction angle

and here it uses the index of refraction.

And the index of refraction really just tells you

it's just the ratio of the speed of light to the actual velocity.

So something where light travels really slowly

where light travels really slowly,

this will be a smaller number.

And if this is a smaller number,

this is a larger number.

And we actually see it here.

And you're going to see a little tidbit of the next video

right over here.

But here's a bunch of refraction indices

for different materials.

It's obviously 1 for a vacuum, because for a vacuum

you have the refraction index is going to be c

divided by the speed of light in that material.

Well, in a vacuum it's traveling at c.

So it's going to be 1.

So that's where that came from. And you can see in air,

the speed is only slightly smaller,

this number's only going to be slightly smaller

than the speed of light in a vacuum.

So in air, it's still pretty close to a vacuum.

But then for a diamond, it's traveling a lot slower.

Light is travelling a lot slower in a diamond

than it is in a vacuum.

Anyway, I'll leave you there,

we're going to do a couple more videos,

we're going to do more examples using Snell's Law.

Hopefully you got the basic idea of refraction.

And in the next video, I'll actually use this graphic right here to help us visualize

why it looks like the straw got bent.