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$\cdot$ The lens of the eye. The crystalline lens of the human eye is a double-convex lens made of material having an index of refraction of 1.44 (although this varies). Its focal length in airis about 8.0 $\mathrm{mm}$ , which also varies. We shall assume that the radii of curvature of its two surfaces have the same magnitude. (a) Find the radii of curvature of this lens. (b) If an object16 $\mathrm{cm}$ tall is placed 30.0 $\mathrm{cm}$ from the eye lens, where wouldthe lens focus it and how tall would the image be? Is thisimage real or virtual? Is it erect or inverted? (Note: The results.obtained here are not strictly accurate, because the lens isembedded in fluids having refractive indexes different from that of air.)

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a) 7.04 $\mathrm{mm}$b) $s^{\prime}=\frac{60 \mathrm{cm}}{73}=0.822 \mathrm{cm}$The image is 0.438 $\mathrm{cm}$ tall and is erect

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

University of Washington

Simon Fraser University

University of Winnipeg

Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

11:16

The crystalline lens of th…

06:56

03:03

11:12

Crystalline lens of the ey…

06:17

The cornea behaves as a th…

04:46

05:29

Two lenses are used to cre…

18:26

The radii of curvature of …

02:17

Measurements on the cornea…

03:45

The cornea as a simple len…

Okay, so this problem is about the lens of the eye, and so it's a double convex lens, so I'll go ahead and drawl it like this. And it has an index of refraction of 1.44 So and is equal toe one point for four. And, um, the focal length is eight millimeters, so eat groups and the radius of curvature has the same magnitude, and then we want to find the radius of curvature of the lens. So to do that, we can use our creation than lens of creation, which is won over half is equal. Thio n minus one times one over r one. I'm not plus minus one over r two, okay. And so these are the same. So that's gonna be on minus one, all multiplied by, um, two over are. And so if we want to solve for are we got that? That's equal to, um, half times and minus one. It's minus times two. So I'm gonna go ahead and plug that into a calculator and see 16 times 160.44 7.4 millimeters. Okay. And then what else does the question I ask if the object is placed, so we know that's object to 16 centimeters tall. Gonna do this on another page? Um, why is 16 centimeters and we know that it's position is 30 centimeters, so us is equal toe 30 centimeters, and and we won't basically just want to know where it's focused and how tall the image would be. And so the F is equal to eight millimeters. I'll go ahead and transpose out here, so af is equal. Thio point to those 0.8 millimeters now eight millimeters. So that's point eight centimeters, and Okay, great. So now I can use that then lens equation to get us prime the position of the image. So we know one of us plus one over s prime is equal to one over half. So we get hit one over s prime, bring this to the other side at the fractions, and then cross multipliers some other version of that algebra. Um, we'll give you half times us divided by, uh, minus us. Did I do that in my head? Right. Oh, Whoops. To Owen as prime equals, bring that over us. It would be one of her half. I'm just gonna read, write it out, having trouble visualizing it. So one over us prime equals one over F minus one over s. And then yeah, then a B s minus f and then flip it. Okay, so I was wrong down here, so that's gonna be s minus f great and plugging in f and s. Is this something I could do in my head? I can't. Okay, 30 times plain age divided by, um 29.2. I got 1.25 centimeters. So that's where the image gets focused and makes sense. And it's such a short distance because it needs to reach your cornea, um, toe to your brain on. So now we want to get the height of the image so we can do why? Over why? Prime equals minus Um Oh, oops. That should be. That's prime over s. Excuse me. A y prime over. Why you do this? I'll go ahead and to block this off. Now we're trying to find the height. So s prime negative s prime over asked equals y prime over. Why and why? Prime is therefore why times us crime groups don't forget the negative divided by us. So I'm gonna plug that into a calculator. Okay. 1.25 provided by Bernie and everyone I multiplied by the height of the original. Just 16 on dhe bra means that the average height is 0.667 Thank you. Centimeters. Okay, let's see him getting different answers. I'm gonna pas this and, um reinvestigate. Okay? I need a calculator error when I calculated as prime. So let me go ahead and fix that. Um, so I mean, yeah, it was just a calculator error. So if I re calculated, I got 0.8 to 2 centimeters. And then if I go ahead and redo this calculation, see what I got? So 0.8 to 2 two divided by Bernie. Well, supplied by 16. I got point for 38 centimeters. So when we were by Assad. Great. And what else is asked? Um, that's the height. And then if s prime is positive. The images Riel thinks you really e think all like you would have to be really like the photons would really have to focus on your cornea for, um, that's right. Part of the eye. You're the photons would have to focus to create an image that your mind could read. And, um so is it Inverted. So magnification is negative s over s prime and us and as primer both positive, um, and therefore magnification negative. And therefore it's inverted. So I'll go ahead and write that down. So it's inverted and huh? No pause this role, okay? Yeah, I stand by. My answer is that was this double checking everything.

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