Snell's law - Wikipedia
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 . Reflected light obeys the law of reflection, that the angle of reflection equals the angle of incidence. For objects such as mirrors, with surfaces. An inspection of the data above reveals that there is no clear linear relationship between the angle of incidence and the angle of refraction. For example, a.
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. Of the four materials present in the above diagram, air is the least dense material lowest index of refraction value and diamond is the most dense material largest index of refraction value. Thus, it would be reasonable that the most refraction occurs for the transmission of light across an air-diamond boundary.
In this example, the angle of refraction is the measurable quantity that indicates the amount of refraction taking place at any boundary. A comparison of the angle of refraction to the angle of incidence provides a good measure of the refractive ability of any given boundary. For any given angle of incidence, the angle of refraction is dependent upon the speeds of light in each of the two materials. The speed is in turn dependent upon the optical density and the index of refraction values of the two materials.
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'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.
The Angle of Refraction
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. 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 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.
The Angle of Refraction
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.
The reflection and refraction of light
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. 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. If the magnification is positive, the image is upright compared to the object; if m is negative, the image is inverted compared to the object.
Sign conventions What does a positive or negative image height or image distance mean? To figure out what the signs mean, take the side of the mirror where the object is to be the positive side. Any distances measured on that side are positive.
Distances measured on the other side are negative. When the image distance is positive, the image is on the same side of the mirror as the object, and it is real and inverted.
When the image distance is negative, the image is behind the mirror, so the image is virtual and upright. A negative m means that the image is inverted. Positive means an upright image. Steps for analyzing mirror problems There are basically three steps to follow to analyze any mirror problem, which generally means determining where the image of an object is located, and determining what kind of image it is real or virtual, upright or inverted.
Step 1 - Draw a ray diagram. The more careful you are in constructing this, the better idea you'll have of where the image is. Step 2 - Apply the mirror equation to determine the image distance. Or to find the object distance, or the focal length, depending on what is given. Step 3 - Make sure steps 1 and 2 are consistent with each other. An example A Star Wars action figure, 8. Where is the image? How tall is the image? What are the characteristics of the image? The first step is to draw the ray diagram, which should tell you that the image is real, inverted, smaller than the object, and between the focal point and the center of curvature.
The location of the image can be found from the mirror equation: The image distance is positive, meaning that it is on the same side of the mirror as the object. This agrees with the ray diagram. Note that we don't need to worry about converting distances to meters; just make sure everything has the same units, and whatever unit goes into the equation is what comes out. Calculating the magnification gives: Solving for the image height gives: The negative sign for the magnification, and the image height, tells us that the image is inverted compared to the object.
To summarize, the image is real, inverted, 6. Example 2 - a convex mirror The same Star Wars action figure, 8. Where is the image in this case, and what are the image characteristics? Again, the first step is to draw a ray diagram. This should tell you that the image is located behind the mirror; that it is an upright, virtual image; that it is a little smaller than the object; and that the image is between the mirror and the focal point.
The second step is to confirm all those observations. The mirror equation, rearranged as in the first example, gives: Solving for the magnification gives: This gives an image height of 0. All of these results are consistent with the conclusions drawn from the ray diagram. The image is 5. Refraction When we talk about the speed of light, we're usually talking about the speed of light in a vacuum, which is 3.