Snell's Law - Refraction Calculator | Science Primer
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 . Snell's law gives the relation between the angle of incidence (θ1), the angle of The angles of incidence and refraction are the angles. ni = the refraction idex of medium containing the incident ray Try the Snell's Law - refraction practice problems to test your understanding of the calculations.
Glass has a higher refractive index than air. When a beam of white light passes from air into a material having an index of refraction that varies with frequency, a phenomenon known as dispersion occurs, in which different coloured components of the white light are refracted at different angles, i.
The different colors correspond to different frequencies. The refractive index of air depends on the air density and thus vary with air temperature and pressure.
Since the pressure is lower at higher altitudes, the refractive index is also lower, causing light rays to refract towards the earth surface when traveling long distances through the atmosphere.
This shifts the apparent positions of stars slightly when they are close to the horizon and makes the sun visible before it geometrically rises above the horizon during a sunrise. Heat haze in the engine exhaust above a diesel locomotive. Temperature variations in the air can also cause refraction of light.
This can be seen as a heat haze when hot and cold air is mixed e. This makes objects viewed through the mixed air appear to shimmer or move around randomly as the hot and cold air moves. This effect is also visible from normal variations in air temperature during a sunny day when using high magnification telephoto lenses and is often limiting the image quality in these cases. Mirage over a hot road. Air temperature variations close to the surface can give rise to other optical phenomena, such as mirages and Fata Morgana.
Most commonly, air heated by a hot road on a sunny day deflects light approaching at a shallow angle towards a viewer. This makes the road appear reflecting, giving an illusion of water covering the road.
Water waves[ edit ] Water waves are almost parallel to the beach when they hit it because they gradually refract towards land as the water get shallower. Water waves travel slower in shallower water. This can be used to demonstrate refraction in ripple tanks and also explains why waves on a shoreline tend to strike the shore close to a perpendicular angle. As the waves travel from deep water into shallower water near the shore, they are refracted from their original direction of travel to an angle more normal to the shoreline.
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. 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.Snell's law of Refraction
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 vand 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, orkilometers per second, or million meters per second--let me write that-- so c is the speed of light in a vacuum, and that is equal to it's not exactlyI'm not going into significant digits-- this is true to three significant digits million meters per second.
This is light in a 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, or refraction index. And it's defined for any medium, for any material.
The Angle of Refraction
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.
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.
BBC Bitesize - Higher Physics - Refraction of light - Revision 3
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.