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Current time:0:00Total duration:12:57

Diopters, Aberration, and the Human Eye

Video transcript

here's something confusing if I showed you two lenses that had two different focal lengths one had a little focal length one had a big focal length and asked you which one of these is more powerful which lens has a higher power you might be confused about what power means but if you had to pick I think a lot of people would probably pick this lens down here because we automatically think bigger means more powerful so a bigger focal length means that it's more powerful that but that doesn't really make a lot of sense because let me show you what happens if we send in parallel light rays into these lenses well what do they do with these light rays we know what they do they send light rays to the focal point because that's what convex lenses do so it'll look something like this so this light ray gets sent there that gets set there this one through here and this one through here that's what happens with that lens what happens down here this lens isn't going to bend the light as much if your focal length is farther away look it it's bending the light yes but the light has not been impacted its original trajectory has not been as influenced as the other lens up here with the smaller focal length so it turns out lenses that have a small focal length will actually have more a greater impact on the trajectory of the light then lenses do with a larger focal length imagine putting this focal length all the way out at infinity well then it wouldn't really affect the light at all the light would just continue straight through because the amount its bending is hardly anything so there's a little weird but small focal length means a powerful lens so rather than talk about focal length optometrist and ophthalmologist often talk about lens power so the lens power is just defined to be this isn't power like joules per second this is lens powers defined to be 1 over the focal length and so if you're using SI units we'd have 1 over meters and that's given a special name that's called diopters so a 1 over a meter is called a diopter and this is what optometrists and ophthalmologists use to measure lens power in its represented with a capital D this makes a little more sense because if you're diopter measurement is large that means powerful lens and if you're diopter measurement is small that means not as powerful of a lens and so in other words if this focal length up here was 10 centimeters well I'd have to convert it to meters so 10 centimeters is 0.1 meters and then to get the power the power for this lens would be 1 over the focal length and meters so I'd have one over point 1 meters and that would mean this is 10 a 10 diopter lens it's supposed to be a d-10 diopter and down here if this one was more like 50 centimeters I'd say that the power is 1 over F I got to convert to meters so 1 over 0.5 meters and I'd get to diopter or to 1 over meters so a diopter has units of 1 over meters or meters to the negative 1 now I'm kind of lying a little bit spherical lenses don't actually send their light rays exactly through the focal point not all of them if you're sending parallel light rays like this through the whole face of the lens some of them are going to miss a little bit and it's called spherical aberration so another thing that you'd be interested in if you're trying to craft precise lenses for a specific purpose is the idea of spherical aberration let me show you what that's all about so let me hide these so what's supposed to happen parallel light rays are supposed to get sent exactly through the focal point boom right there what actually happens is parallel light rays get sent the ones on top get bent a little bit more and they might focus around this point and the ones closer into the center of the lens gets sent over here and so the spherical convex lens kind of focuses all the light to a point but it creates a little bit of a blur here so this is called spherical aberration and this is an inherent problem with spherical lenses the light to get sent through the top gets bent a little bit more than the light they get sent more toward the middle and so you've got this problem this is a problem if you have a highly precise situation that you need to create an image for it might get a little bit blurry because of spherical aberration so you might wonder why does this spherical aberration happen it has to do with the fact that you know how we're always calling these thin lenses you might wonder why are we always calling them thin lenses why do they got to be thin it's because if they're thin all these angles involved for these normal lines are going to be small and if the angles are small that's a good thing because in physics physicists love this one here's a trick we like playing sine theta for small angles is approximately just theta and so there's all kinds of approximations here that you can use if the lenses are thin and you get that they all go basically through the focal point but there's a difference between basically going through the focal point and exactly going through the focal point and the farther you get up here the larger this angle is going to be the more deviation you're going to get it's just a problem inherent to this spherical lens the problem is it's easy to make spherical lenses I mean it's easy to make a perfectly spherical shape if you wanted to make one that did send them exactly through the center it'd be harder to do you'd have to pick a different shape because spheres just don't cut it in that case spherical aberrations not even the only type of aberration there's other kinds of aberration one of them is chromatic aberration and as the name suggests this has to do with color and remember dispersion with lenses or any material dispersion says that some colors Bend more than others so some colors experience a higher index of refraction red turns out experiences a smaller index of refraction so these red rays would get sent that get bent a little bit less than yellow so they might meet up there and blu-rays blue get spent more higher frequency light gets bent more and so you'd get these colors separating so this is another problem with spherical lenses or any type of lenses you might get some sort of chromatic aberration so these are things to look out for if you're trying to create a precise optical instrument one of the most precise optical instruments is the human eye and in the human eye you have a lot of parts up front you've got the cornea this acts like the main lens this is the front lens here this does most of the bending of the light but you've also got this inner lens that's just called the lens and this inner lens is more adjustable this can sort of make fine adjustments to what you're looking at if you're depending on how close something is to your eye this can adjust and these ciliary muscles are muscles that can exert a force on this lens and can change the shape of it this is bendable this inner lens is bendable and depending on what distance away the object is these ciliary muscles can change the shape of this lens to make sure that the image is formed right on your retina this back wall acts as the screen of your eye and this is where you want the image to form if you form a nice clean precise image on your retina the optical nerve can take that information to your brain and you get a nice clean image of whatever it is you're looking for maybe it's a tree now the weird thing is so here's your tree this may be you see this but here's the weird thing you've got this cornea and this inner lens are both convex and if you're going to see a real image that's actually projected on a screen here this is actually going to be an upside-down image your tree image that forms actually on your retina is an upside-down real image so your optical nerve sends that information your brain somewhere in your brain it flips it over and then you get a clean image of a tree that's right-side up all right so if you were looking at afar a tree let's say the tree was really far away and these light rays were coming in basically parallel you'd want to make sure your cornea and your inner lens were able to focus these light rays from some point on the tree straight into the retina and you form a nice clean image at the retina so that's good let's say you're able to do that just fine you get a clean image of this tree what if you got a little bit closer maybe you get a little closer and now and now the image isn't so clean so you got this tree here you're looking at a particular part of it maybe you're looking at this part right here you're a little closer this part comes in here we're looking at light rays out of here it's not going to get been as much your ciliary muscle is going to have to adjust them maybe they can't just maybe they can't cut it and this forms an image back here but that's bad that's bad because if you form an image behind your retina that's going to be blurry you're not going to see the nice clean image here you're going to get this weird blurred out image so your ciliary muscle is going to try to compensate but maybe they can't so this person might need glasses this person if they were able to see the faraway tree just fine but things up close we're hard for them to focus on we'd call this person farsighted so farsighted people can see faraway stuff just fine but when it's too close they can't focus on it so what do we do we add another lens in here we're going to add a lens that tricks our i CRI this farsighted person was good at seeing stuff far away so I'm gonna try to take this tree this object I'm gonna try to make an image of it farther away so how do I do that I'm going to prescribe this person a convex lens because the convex lens will create a virtual image of the tree at some farther away point we trick our eye now it can focus a little better we can take this image and bring it up to our retina get a nice clean image of the tree so that's for a farsighted person for a nearsighted person let me get another image in here nearsighted people can see stuff near just fine and it's the far stuff that they have trouble with so for a nearsighted person focusing on this tree up here that's no problem they can focus on this just fine they get a nice clean image of the tree right at the spot where it's supposed to be at at the retina you get a nice clean image but if you move the tree further away they'd have trouble so we need to take this tree I'm going to take it right here so I'm going to take this tree and I'm going to move it farther away now the eye has trouble seeing it and so now that I is going to form an image maybe the eye forms the image up here that's not good we need to bring this back over to this way and so we'll have to prescribe the lens this person was able to see near stuff just fine so again we're gonna have to trick our eye we take this object we need a lens the next hour I think that this objects closer than it is and we'll prescribe this person a diverging lens or a concave lens and this lens is going to make a virtual image of this tree that's a little bit closer than the actual object was so now our light that comes in to our eye once it gets to our eye I'm neglecting a lot of bending going on here we can actually get this light to focus right on our retina which is what we wanted it to do and we get a nice clean image so depending on whether you're near-sighted or farsighted you'd prescribe someone either so nearsighted get diverging lenses farsighted people get converging lenses and that's one way you can trick the eye and make it so you can see a nice clear image