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Anderson Video - Contact Lens Example

Professor Anderson
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<font color="#ffffff">Let's take a look at the next one, number 11, and this is the</font> <font color="#ffffff">problem with Alice being farsighted and she can't see objects</font> <font color="#ffffff">that are closer to her eye than 80 centimeters.</font> <font color="#ffffff">What is the refractive power of the contact lenses that will</font> <font color="#ffffff">enable her to come from comfortably see objects at a distance of 25 centimeters</font> <font color="#ffffff">from her eye? Okay, so this is a contact lens problem</font> <font color="#ffffff">and remember a contact lens is just another lens that you put right in front of your eye.</font> <font color="#ffffff">So let's draw the issue here, here's her eyeball</font> <font color="#ffffff">and she can see things that are 80 centimeters away, no problem.</font> <font color="#ffffff">Okay, which means that she can focus that image onto her retina,</font> <font color="#ffffff">but when that object comes in a lot closer,</font> <font color="#ffffff">to 25 centimeters,</font> <font color="#ffffff">now she can't focus it on her retina anymore, it in fact is gonna focus</font> <font color="#ffffff">behind her eyeball. Okay.</font> <font color="#ffffff">So this is of course somebody that is what? Farsighted or nearsighted?</font> <font color="#ffffff">Farsighted, Alice is farsighted because she can see things that</font> <font color="#ffffff">are far away but she can't see things that are close.</font> <font color="#ffffff">So right off the bat, if you're going to fix Alice's eyeballs to read,</font> <font color="#ffffff">do you want to use positive lenses or negative lenses?</font> <font color="#ffffff">>> (student speaking) Positive.</font> <font color="#ffffff">Yeah, you need to use a positive lens in this case,</font> <font color="#ffffff">reading glasses are positive lenses. All right, so we're going to take this picture now </font> <font color="#ffffff">and we're going to add a positive lens. So here's her eyeball, I'm going to put a</font> <font color="#ffffff">contact lens right on her eyeball and now the image is formed on the retina.</font> <font color="#ffffff">So, when you put two lenses together</font> <font color="#ffffff">do you add their focal lengths?</font> <font color="#ffffff">If I have f1 and f2, is the resulting focal length going to be f1 plus f2?</font> <font color="#ffffff">No, that doesn't sound right because that would be a much longer focal length lens.</font> <font color="#ffffff">And I know that if I put a magnifying glass next to my eyeball.</font> <font color="#ffffff">Right? It's going to act like a shorter focal length lens.</font> <font color="#ffffff">So, when you add two lenses, you in fact add their powers.</font> <font color="#ffffff">And power is one over the focal length,</font> <font color="#ffffff">and remember the units are one over meters which is diopters.</font> <font color="#ffffff">So, in this new case we need to figure out how much power to add in a contact lens</font> <font color="#ffffff">and to do that, we need to know the power of her eyeball in the first case. Okay.</font> <font color="#ffffff">Okay, so what is the image distance?</font> <font color="#ffffff">The image distance is the size of the eyeball which is 25 millimeters</font> <font color="#ffffff">and therefore in this case we have 1 over F, bless you, equals 1 over d o plus 1 over d i,</font> <font color="#ffffff">and this is -- we'll call this f of her bare eyeball.</font> <font color="#ffffff">D o is 80 centimeters, so that's 1 over 0.8 meters.</font> <font color="#ffffff">D i is 25 millimeters, which is 0.025 meters</font> <font color="#ffffff">and if you</font> <font color="#ffffff">calculate this you are in fact calculating the power of the bare eyeball.</font> <font color="#ffffff">And what do you get if you do that? You can almost ignore the 1 over 0.8,</font> <font color="#ffffff">this is going to be a much bigger number but punch it into your calculator anyway</font> <font color="#ffffff">and tell me what you get for the power of her bare eyeball.</font> <font color="#ffffff">>> (student speaking) 0.0202</font> <font color="#ffffff">>> No, because this is going to be something like 40, right?</font> <font color="#ffffff">And this is going to add another 1.2 to it,</font> <font color="#ffffff">so I'm gonna say that you should get somewhere around there.</font> <font color="#ffffff">Anybody get that in their calculator?</font> <font color="#ffffff">>> (student speaking) 41.2.</font> <font color="#ffffff">41.2? Okay, so 41.2 is the power of her bare eyeball but now we're going to add</font> <font color="#ffffff">a lens to the system right in front of her eyeball</font> <font color="#ffffff">and we have a new d o.</font> <font color="#ffffff">D o is now 25 centimeters. We have the same d i because it's the size of the eyeball,</font> <font color="#ffffff">25 millimeters, and so now we can calculate the power of the contact</font> <font color="#ffffff">plus bear eyeball system,</font> <font color="#ffffff">and that is going to be 1 over F of the contact plus bear eyeball system</font> <font color="#ffffff">and that is 1 over 0.25 plus 1 over 0.025,</font> <font color="#ffffff">and what do we get if we do that?</font> <font color="#ffffff">Well, this is still 40 and this is 1 over 1/4 which is 4, so I'm gonna say it's 44.</font> <font color="#ffffff">Is that what you guys got? Okay, these are both diopters.</font> <font color="#ffffff">So the bear eyeball was 41.2, the system together was 44 and since you can add powers,</font> <font color="#ffffff">what is the power of the contact lens? It's just the difference.</font> <font color="#ffffff">It's going to be the power of the contact with the bear eyeball minus the power of the bear eyeball:</font> <font color="#ffffff">44 minus 41.2 and that's going to equal 2.8 diopters</font> <font color="#ffffff">and that's a positive number, and if we look at the answers</font> <font color="#ffffff">one of them is really close to 2.8, it is answer B, it says 2.75, so there must have been a</font> <font color="#ffffff">little bit of extra digits here, somewhere that we missed.</font> <font color="#ffffff">Okay, and that sounds like a reasonable number, right?</font> <font color="#ffffff">When you go to get your prescription what does it say? It says plus 2.8</font> <font color="#ffffff">or plus 3.5 or negative 3 or negative 2</font> <font color="#ffffff">and that's the power that you're adding with this contact lens.</font>