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$\cdot$ For each thin lens shown in Figure $24.49,$ calculate the loca-tion of the image of an object that is 18.0 $\mathrm{cm}$ to the left of thelens. The lens material has a refractive index of $1.50,$ and theradii of curvature shown are only the magnitudes.

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a) 36 $\mathrm{cm}$ to the right of the lensb) 180 $\mathrm{cm}$ to the left of the lensc) 7.2 $\mathrm{cm}$ to the left of the lensd) 13.84 $\mathrm{cm}$ to the left of the lens

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

University of Washington

Simon Fraser University

Hope College

McMaster University

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.

14:59

For each thin lens shown i…

05:37

01:15

6. A convex-concave lens h…

05:59

Consider a thick biconvex …

02:13

A thin lens is made of gla…

01:42

The left face of a biconve…

00:59

A The left face of a bicon…

02:38

02:46

to solve this problem. We really only need the thin lens equation. Ah, which says that one of her object distance plus one over image distance is equal to one over focal ink, which in turn is equal to refractive index of the lens minus one times one over a radius of curvature of one end by this one over a radius of curvature at the other end. And so the all important sign conventions here is that our warner to R R would be positive if that side his con effects. Okay, so your side looks like this then our asse positive. Your side looks like that are a cz negative. It's a simple is that But it is. It is easy to forget and it is what remember? Okay, so So we have That s the image is formed 18 centimeters to the left middle and sass is 18 centimeters and so she want as prime. You have one. Arrest Prime Michel's one over F minus one over 18. Sentiments furthermore, we have on is 1.5 so and minus one is ah, 0.5 on DH. That's it. Now we now we tackle the problems individually the parts individually. So part, eh has the lens looking like this. Kind of. So we look at this end. Okay. Is it convex? Is it Is it that shaped? Yes, it isthe So this send this positive discern is a convex. No, it's not. It's Kong case, so that is negative. So stop in this case, you have one of Raph equals 10.5 minutes. One times one of her are one, remember is positive. Plus our one call it minus minus. R too. Our one is a cz positive. Here is goingto is this, um And so you have one of her 10 centimeters minus one over minus 15 centimeters. Because remember, this side is negative s o. This works out to be one over 12. So one of our local linked s So that means that one over us prime is one over 12 minus one over 18. Implying that s prime image. Distance is, uh, dirty. Six centimeters, 36 centimetres. So you have a positive us prime, meaning that the images to the opposite side of the lens as the object is so images 36 centimeters right of the lens. Okay. Moving on to part. Uh, Herbie, you have Ah, this kind of situations and this is again the same is this of one side. So are one. It's positive are two, on the other hand, has no curvature, so are too Ah, feel recall is approximate is infinity as as intimate The temperature is extremely, extremely large. So where you have here is that one of grass is equal to again 0.5 times again one over 10 minus one over infinity and that is just zero. So you're left to it from one over pass of ah were over 20. And so this implies that one arrest prime is whatever 20 minus one over 18. Therefore, as prime is negative 1 80 centimeters. So that's a negative moving. It's on the same side of the lens as the image. So his prime is 1 80 centimeters left of lens. All right, on part CV books on part. See, you have a different situation Where where this is what it looks like. There you go, the parts he looks like that. And so as you can see, there's a con cave side on this end and sound And so this is negative are one is negative. There's a con. So there's a conflict side on this and actually so are, too. It's positive here, right? So one of reps is 0.5 times one over negative, 10 minus one over 15. There's a positive 15 because of the conquered. All right back side are convex backside. And so this works out to be one of our f is negative. One over 12. And so one arrest Prime is just negative. One of 12 it's one over 18. And so as prime is again a negative number. So that's actually seven points of this image of 7.2 centimeters again left of length. All right. And finally, for part d, we have this kind of situation, and so here, as well as we saw in part See, you've now come cave, huh? Front side. So are one is negative. Ah, but you that's right. But unlike part seriously, you don't have a convex back side. So are two is also con cave. So are too is also making so in this case, one over at vehicles 10.5 times one of her negative 10 minus one over and negative 15. Okay, and that's one negative. One over 60. So we have won over as prime is negative one over 16 by this one over 18 implying that s crime works out to be a negative 13.8 centimeters. And again, that's a negative. Meaning that image of 13.8 centimeters. Ah, left of the lens, and that is that's that.

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