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The cornea as a simple lens. The cornea behaves as a thin lens of focal length approximately $1.8 \mathrm{cm},$ although this varies a bit. The material of which it is made has an index ofrefraction of 1.38 and its front surface is convex, with a radius of curvature of 5.0 $\mathrm{mm}$ . (a) If this focal length is in air, what is the radius of curvature of the back side of thecornea? (b) The closest distance at which a typical person can focus on an object (called the near point) is about 25 $\mathrm{cm}$ ,although this varies considerably with age. Where would thecornea focus the image of an 8.0 -mm-tall object at the near point? (c) What is the height of the image in part (b)? Is this image real or virtual? Is it erect or inverted? (Note: The results obtained here are not strictly accurate, because, on one side, the cornea has a fluid with a refractive index different from that of air.)

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a) 19.587 $\mathrm{mm}$b) 1.94 $\mathrm{cm}$c) $-0.62 \mathrm{mm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

Rutgers, The State University of New Jersey

University of Washington

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.

04:46

The cornea behaves as a th…

06:17

06:34

05:54

The cornea of the eye has …

09:55

09:25

$\cdot$ The lens of the ey…

04:20

Focus of the eye. The corn…

07:54

02:16

As objects are moved close…

11:12

Crystalline lens of the ey…

01:36

$\cdot$ The cornea as a th…

All right. So the cornea is treated as a thin lens here, and so that then leads equation applies. One of her focal length is equal to refractive index minus one times one of radius of curvature of fun and minus one. Overuse. Um, coach of the back it And it is this our two that we want here in part eso let's we're angels equation and write one of our one writes or one of our two is equal to one over f times one over and minus one. That's just, um, pulled to the left hand side on dso One of our two is just one of her. Are one minus this whole thing of one of our aft times one over and minus one. Okay, on DSO. One of our one is five millimeters less of directing staff. Trip to millimeters. Ah f is 1.8 centimeters. Ah, so that will be 1.8 centimeters are about 18 millimetres. 18 millimeters. Oops. Okay, so that's 18 millimeters, and that's and er multiplied by one over one point 38 minus 11 country. It was a given refractive index. That's one of our two and So this implies that are too Take a reciprocal. What you've got get is 18.6 millimeters or 1.86 centimeters. Part B wants the image distance and so he is one over f equals one of us, plus one over X prime and one of us plus one arrest prime So hopes Assassins as prime there on dso one arrest as primarily once So could be right. This when I were f minus one over R s and half again is eyes one little strain two centimeters from 20.8 centimeters. That's F and s image distances 20 Object distance 25 And so we get that as prime is 1.9 centimeters. Finally for part. See Ah, we first configure out magnification shows negative image distance over object distance. So that's negative. 1.9 over 25. That's negative. 250.76 This means that the images, um inverted lips on inverted, um, and then because it's negative and then em is also God, em is also Ah, negative. Whoops. Positive. Why prime over why My prime is what we want. The image height. So that's m times. Why. So that's negative 0.76 times eight millimeters. And so this comes out to be negative 80.61 millimeters. So it's a D magnified image and then ask prima's positive. Let's be found in part B. So this is ahh, real image.

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