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Physics33. Geometric OpticsThin Lens And Lens Maker Equations

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