33. Geometric Optics
Ray Diagrams For Lenses
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<font color="#ffffff">Alright let's ask you a question: why can't you focus underwater?</font> <font color="#ffffff">Okay, let's say you go swimming, right? Underwater and you're not wearing a mask.</font> <font color="#ffffff">Your're just floating around down here.</font> <font color="#ffffff">Here's your big old eyeballs you're having a good time.</font> <font color="#ffffff">And you're trying to see this fish but it looks all blurry, okay?</font> <font color="#ffffff">The fish looks blurry. You have a hard time focusing underwater.</font> <font color="#ffffff">Why is that?</font> <font color="#ffffff">To understand this we need to think about what's happening</font> <font color="#ffffff">to the rays of light that are coming from the fish to our eyeballs.</font> <font color="#ffffff">Okay, and let's draw a couple pictures here.</font> <font color="#ffffff">Here's your eyeball.</font> <font color="#ffffff">And when parallel rays come in, they are focused to a point at the back of the retina.</font> <font color="#ffffff">Okay? At the back of your eyeball at the retina.</font> <font color="#ffffff">But let's draw it in a little more detail to see what happens in this bending at the cornea.</font> <font color="#ffffff">This is the cornea of your eyeball</font> <font color="#ffffff">and when this parallel ray comes in, it's going to hit this first interface.</font> <font color="#ffffff">This is air out here. This is your cornea as the rest of your eyeball.</font> <font color="#ffffff">And so there's going to be bending at that first surface. </font> <font color="#ffffff">The light is going to bend at the cornea.</font> <font color="#ffffff">And it's that bending at the cornea that's going to allow it to focus on the back of your eyeball,</font> <font color="#ffffff">but why does it bend there? Alright.</font> <font color="#ffffff">It bends because Snell's law says n-air sine-theta, air equals n-cornea sine-theta cornea.</font> <font color="#ffffff">And there is a different index of refraction between the air and the cornea </font> <font color="#ffffff">and that means that theta has to change.</font> <font color="#ffffff">Okay? It's going to bend towards the normal since the cornea is curved.</font> <font color="#ffffff">Those parallel rays will bend inward towards their relative normals .</font> <font color="#ffffff">But what happens when you're underwater?</font> <font color="#ffffff">When you're underwater, here come the light rays in, here's our cornea.</font> <font color="#ffffff">There's our eyeball and now we're not in air anymore we are in water.</font> <font color="#ffffff">And so Snell's law says that n of water sin theta of water</font> <font color="#ffffff">equals n of the cornea sin theta of the cornea.</font> <font color="#ffffff">And so it's going to bend if those are different </font> <font color="#ffffff">and it's not going to bend if they are the same.</font> <font color="#ffffff">And what happens is those are nearly the same.</font> <font color="#ffffff">N water is nearly the same as n of the cornea.</font> <font color="#ffffff">And therefore, theta in the water is nearly the same as theta in the cornea.</font> <font color="#ffffff">Things don't focus.</font> <font color="#ffffff">And so you can't see under water. You can't focus very well under water.</font> <font color="#ffffff">Now, anybody know why this would be?</font> <font color="#ffffff">Why would your cornea have nearly the same index of refraction as water? </font> <font color="#ffffff">Any ideas?</font> <font color="#ffffff">Because you guys are made up of water, okay?</font> <font color="#ffffff">You are mostly water and so the cornea has</font> <font color="#ffffff">nearly the same index as water because a lot of it's made of water, right?</font> <font color="#ffffff">Sort of this gelatinous stuff but it's the same idea, okay?</font> <font color="#ffffff">So how do you fix this problem?</font> <font color="#ffffff">When you're swimming under water and you do want to see those fish,</font> <font color="#ffffff">how do you fix the problem? </font> <font color="#ffffff">You get an air water interface again by putting on a mask.</font> <font color="#ffffff">And by putting on that mask you put a little air in front of your eyeballs.</font> <font color="#ffffff">And when the light rays come now and they go to the air cornea interface</font> <font color="#ffffff">they can bend and come to a focus.</font> <font color="#ffffff">Alright? This is the whole reason for the mask.</font> <font color="#ffffff">is just to provide a little air next to your eyeballs.</font> <font color="#ffffff">In fact you don't need a mask if there was another way to provide air right there,</font> <font color="#ffffff">you can do it, and you've seen this before, right?</font> <font color="#ffffff">If you take a big bucket and put it over your head and you go underwater </font> <font color="#ffffff">and now there's an air gap between the water level and your eyeballs, then you can see just fine again.</font>
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