# Reflection and Refraction

by Jared Rovny

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00:01 We’ve discussed now how electromagnetic waves work. So, we’re ready to enter into the new topic of optics, how these electromagnetic waves, this light behaves as it bounces around or goes from one medium to the next. We’ll start this discussion on optics by discussing reflection and refraction, these two sort of joint properties. In the overall topic of optics after we’ve begun with the reflection and refraction, we’ll talk about mirrors and lenses, and then finally move to some optical instruments and how they use the principles that we’ll discuss in order to do what they do, whether they’re zooming into small things or looking at very big, very far away things. We’ll start with the definitions of reflection and refraction.

00:44 First, we’ll need to know that as light is moving through some medium, we’ve already mentioned that the speed of light or the velocity of any wave through a medium only depends on that medium and the properties of that medium. With that said, we know that light isn’t always travelling in a pure vacuum just out in space. Usually, it’s travelling in our context through something like air or water. Through each of these different media, the light’s speed will actually be different as it interacts with all the particles in that medium. We can define for each one of these mediums, whether it’s the air or the water, something called the index of refraction. That is the ratio of the normal speed of light in a vacuum, C to the speed of light in whatever medium it’s travelling through.

01:29 Notice by this definition of the index of refraction N that for a higher N, for a higher index of refraction.

01:37 We mean that the speed of light is slower in that medium. So, a more dense medium like water, for example, would have a higher index of refraction and a lower speed for light to travel through that medium. Secondly, we should start talking about the refraction since we’ve introduced the index of refraction for when a beam enters from one medium into another. Suppose we have a light beam like this one. It’s moving towards the air, in this case starting in a vacuum. When the incident beam hits the air, hits this new medium, it will bend. We talk about the amount of light that goes into the new medium as the transmitted amount of light. This bending effect is part of what the light does but some of the light will also be reflected when it hits the boundary of going into a new medium. So, we have an incident wave which is the light wave that’s going in towards the medium. Then part of that incident wave, that initial wave will bend into the medium.

02:34 Part of it will be reflected from the medium. What we do to describe the incident and reflected or transmitted beams as it goes into this medium is first we draw an access, this dotted green line here.

02:48 This dotted green line, this access is normal to or perpendicular to the surface between the two mediums. Then, given this line and knowing the incident ray and the exiting ray, the reflected ray, we can define an angle of each ray with this horizontal line. We call the incident angle the angle of incidence. We’re calling this θ sub i for the incident angle. Then, we have a reflected angle or the angle of reflection, θ sub r. Lastly, we could also define a transmitted angle, the angle at which the light that goes into the new medium is transmitted into that medium. Again, because the light has bent into that medium, we would expect that the incident angle as you can see here on its way in will be different from the transmitted angle because the light wave bends as it goes into this new medium. The amount of the reflection will decrease as we decrease the incident angle.

03:47 In other words, when we send light more directly into a new medium, less of that light will be reflected and more will be transmitted into that medium. The incident angle and the reflected angle, ignoring right now the transmitted amount of light, are always going to be the same. This sort of follows our intuition that if light hits a surface and bounces off, it will bounce off at the exact same angle that it came in at.

The lecture Reflection and Refraction by Jared Rovny is from the course Geometrical Optics.

### Included Quiz Questions

1. n = c/v
2. n = c²/v²
3. n = √c/√v
4. nsinθ = c/v, with θ the refraction angle of light
5. n = v/c
1. Part of the light is refracted into the water and the rest is reflected at the same angle as it was incident.
2. Part of the light is transmitted and the rest is reflected at twice the angle as it was incident
3. All the light is transmitted into the water
4. Part of the light is transmitted straight into the water without any bending and the rest is reflected at the same angle as it was incident
5. Most of the light is reflected, but some light is transmitted at twice the angle as it was incident
1. The angle between the normal to the surface and the incident ray is equal to the angle between the normal to the surface and the reflected ray.
2. The angle between the incident ray and the reflected ray is always equal.
3. The angle between the normal to the surface and the incident ray is equal to the angle between the surface and the reflected ray.
4. The angle between the surface and the incident ray is equal to the angle between the normal to the surface and the reflected ray.
5. The angle between the incident ray and the surface is always equal to the angle between the surface and the refracted ray.

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