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The thin glass shell shown in Figure 24.44 has a spherical shape with a radius of curvature of $12.0 \mathrm{~cm},$ and both of its surfacesthe center of the mirror along the can act as mirrors. A seed 3.30 $\mathrm{mm}$ high is placed $15.0 \mathrm{~cm}$ fromoptic axis, as shown in the figure.(a) Calculate the location and $\Delta$ FIGURE 24.44 height of the image of this seed. Problem 17 .(b) Suppose now that the shell is reversed. Find the location and height of the seed's image.

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(a) Image is formed 10 $\mathrm{cm}$ in front of the mirror It is inverted and 2.2 $\mathrm{mm}$ tall(b) Image is formed 4.29 $\mathrm{cm}$ behind the mirror It is upright and 0.94 $\mathrm{mm}$ tall

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

Hope College

University of Sheffield

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.

03:37

The thin glass shell shown…

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05:52

09:39

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07:34

The radius of a spherical …

01:05

An object $3.5 \mathrm{cm}…

01:57

(II) An object 3.0 $\mathr…

05:32

A coin is placed next to t…

Okay, so in this question, we have typical ah mirror curved mirror information about it. And we want to get the height and location of the image. And then we want to flip a shell around and see how about changes things. So let's go ahead and start by recording are givens. So the radius of curvature is equal to 12 centimeters and the see it's high is equal to to ah, 3.3 millimeters. So I'll go ahead and convert that to centimeters and say that that's point three three zero centimeters and it's 15 centimeters in the front. So ass is equal to 15 centimeters and are we want to get a gun, All the information about the image. So we want to use our usual creation one over as plus one over us. Prime is too over our you manipulated and solved for one over s prime by subtracting the one over s, you got to over our minus one of us is one over x prime. And then you can, um you either think of it is cross multiplying or just inverting both sides and say that now you can. That s prime is equal to this whole thing to the minus one power. So, um and I guess what I'm doing. Formulas. Why not do the height? So we know that. Why prime over why is equal to us prime over us. Negative s prime over us. So that we know once we get us prime, we can solve for y prime because we have y in us and we get the white crime is minus s prime over ass times. Why? So now I'm gonna go ahead and just plug in. And so for s prime. And, um Ah, why, prime? I'm gonna pause the video while I use the calculator, too. Okay, so I put that into a calculator, and I got that s prime was 10 centimeters playing in the 10 centimeters here, I got that. The new height was 100.22 centimeters, so that would be the answers for part a. And then for part B, you want to answer the use? Um, given that you switched the mirror around. So all that's gonna do is make our go to negative 12.0, centimeters. And so now I'm gonna solve these same plugin Anouar and solved for us prime. And why, Prime? So I'm gonna pause the video while I do that. Okay, So when I put that into a calculator, I got that the new position. Waas at 4.29 in the new height. Waas equal to drum Ruelas, I tab over 0.944 Um, one thing I want to revise over here. I did. I forgot to take the negative sign here. So the height is gonna be negative. 10.22 which just means that it's inverted on them. This one's not inverted. And then, actually, oops. That should also be negative. Um, great. So I'm gonna double check something. Um, you mind for four? Yeah. Okay. Great. Looks good.

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