# Angle of incidence and refraction relationship tips

### The Angle of Refraction

The angle of incidence and angle of refraction are denoted by the following There is a mathematical equation relating the angles that the light rays make with . Student will determine the equation relating the angle of incidence, angle of refraction, and the refractive index of each medium that light Tech Tips: Make sure. Jul 27, Reflected light obeys the law of reflection, that the angle of reflection equals the angle of incidence. For objects such as mirrors, with surfaces.

Light travels the fastest 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. 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. 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? This wheel is going to reach the mud first.

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.

Refraction (2 of 5) Snell's Law, Calculating Angle of Refraction and Angle of Incidence

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. 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 has a center of curvature, C, which corresponds to the center of the sphere it was cut from; a radius of curvature, R, which corresponds to the radius of the sphere; and a focal point the point where parallel light rays are focused to which is located half the distance from the mirror to the center of curvature.

The focal length, f, is therefore: Parabolic mirrors are really the only mirrors that focus parallel rays to a single focal point, but as long as the rays don't get too far from the principal axis then the equation above applies for spherical mirrors. The diagram shows the principal axis, focal point Fand center of curvature for both a concave and convex spherical mirror.

Spherical mirrors are either concave converging mirrors or convex diverging mirrors, depending on which side of the spherical surface is reflective. If the inside surface is reflective, the mirror is concave; if the outside is reflective, it's a convex mirror. Concave mirrors can form either real or virtual images, depending on where the object is relative to the focal point. A convex mirror can only form virtual images. A real image is an image that the light rays from the object actually pass through; a virtual image is formed because the light rays can be extended back to meet at the image position, but they don't actually go through the image position.

Ray diagrams To determine where the image is, it is very helpful to draw a ray diagram.

## Refraction and Snell's law

The image will be located at the place where the rays intersect. You could just draw random rays from the object to the mirror and follow the reflected rays, but there are three rays in particular that are very easy to draw. Only two rays are necessary to locate the image on a ray diagram, but it's useful to add the third as a check.

The first is the parallel ray; it is drawn from the tip of the object parallel to the principal axis. It then reflects off the mirror and either passes through the focal point, or can be extended back to pass through the focal point.

The second ray is the chief ray. This is drawn from the tip of the object to the mirror through the center of curvature. The chief and parallel rays meet at the tip of the image. The third ray, the focal ray, is a mirror image of the parallel ray.

The focal ray is drawn from the tip of the object through or towards the focal point, reflecting off the mirror parallel to the principal axis. All three rays should meet at the same point. A ray diagram for a concave mirror is shown above. This shows a few different things.

### The reflection and refraction of light

For this object, located beyond the center of curvature from the mirror, the image lies between the focal point F and the center of curvature. The image is inverted compared to the object, and it is also a real image, because the light rays actually pass through the point where the image is located. With a concave mirror, any object beyond C will always have an image that is real, inverted compared to the object, and between F and C.

You can always trade the object and image places that just reverses all the arrows on the ray diagramso any object placed between F and C will have an image that is real, inverted, and beyond C. What happens when the object is between F and the mirror? You should draw the ray diagram to convince yourself that the image will be behind the mirror, making it a virtual image, and it will be upright compared to the object.

A ray diagram for a convex mirror What happens with a convex mirror? In this case the ray diagram looks like this: As the ray diagram shows, the image for a convex mirror is virtual, and upright compared to the object.

A convex mirror is the kind of mirror used for security in stores, and is also the kind of mirror used on the passenger side of many cars "Objects in mirror are closer than they appear. A convex mirror will reflect a set of parallel rays in all directions; conversely, it will also take light from all directions and reflect it in one direction, which is exactly how it's used in stores and cars. The mirror equation Drawing a ray diagram is a great way to get a rough idea of how big the image of an object is, and where the image is located.

We can also calculate these things precisely, using something known as the mirror equation. The textbook does a nice job of deriving this equation in section Magnification In most cases the height of the image differs from the height of the object, meaning that the mirror has done some magnifying or reducing.

The magnification, m, is defined as the ratio of the image height to the object height, which is closely related to the ratio of the image distance to the object distance: The diagram below depicts a ray of light approaching three different boundaries at an angle of incidence of degrees.

The refractive medium is different in each case, causing different amounts of refraction. The angles of refraction are shown on the diagram. Of the three boundaries in the diagram, the light ray refracts the most at the air-diamond boundary. This is evident by the fact that the difference between the angle of incidence and the angle of refraction is greatest for the air-diamond boundary. But how can this be explained? The cause of refraction is a change in light speed; and wherever the light speed changes most, the refraction is greatest.

We have already learned that the speed is related to the optical density of a material that is related to the index of refraction of a material.