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An object 0.600 $\mathrm{cm}$ tall is placed 16.5 $\mathrm{cm}$ to the left of thevertex of a concave spherical mirror having a radius of curvature of 22.0 $\mathrm{cm} .$ (a) Draw a principal-ray diagram showing the formation of the image. (b) Calculate the position, size,orientation (erect or inverted), and nature (real or virtual) of the image.

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b) Image is realIt is formed 33 $\mathrm{cm}$ to the left of mirrorIt is inverted and 1.2 $\mathrm{cm}$ tall

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

Hope College

University of Winnipeg

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.

06:49

An object $0.600 \mathrm{~…

03:44

An object 0.600 cm tall is…

09:09

0:00

20:13

A concave spherical mirror…

06:31

An object $1.0 \mathrm{~cm…

01:20

04:15

A concave mirror has a rad…

01:05

An object 5.0 cm tall is 4…

Okay, so we have a Kong caved marriage. Andi, What Kong Kate Moravians is that radius of curvature is politics are stranger than zero thiss means, that's all. So we can find a local inn, Uh, as are over too thie contacts. Cases negative are over to our is given to us is 22 centimeters and divide that by two. You get 11 centimeters for focal. Now we're given the object distance. Basically, the distance here, from the center of the mirror to the to the object s is 16 0.5 centimeters. So this is greater than focal length after, which is 11. Okay. And so when this is the case where object went for a concave mirror object distance is clear. The focal length. We have an image that Israel and inverted meaning the s crime will be, ah, meaning that image will be on the same side as the objects as probably zero and magnification will be negative and rest of zero. So we're pleasantly answering be already. But we will work that out in a second. But it will. It will. This is This is our backdrops were for the raid diagram that I've drawn here. Okay, so here's the May diagram. Object? Oh, here is a vertical height above the plane. See, there's the centre of curvature here. I hear in this intersecting point, that's the sense that the distance from here to the center of the mirror is the radius of curvature are okay. And so already you can see that object distance s which is owed to him eyes less than our which in sea to him. Okay. And then we have f is less than us. So the focal point f over here, Big Gus, uh, is, uh is before oh, before the object. Oh ah, and then the image. Since it is the image since it Israel and inverted it, will this case be beyond the object beyond the courage? So let's let's work that out. Fire all these way diagrams. So I used here the there basics off or the method of obtaining about joining a ray diagram from from section 24.3, the recipe that's given. So we have four different rates. One of them Ray one. By the way, each of the rays are shown by a different color. So too better help understand what's going on. So, rain one Sean and blue eyes is going from the object to the mirror and it and it is parallel to the access. It is parallel to rose to the X to the plane. Um and so that gives us the first, the first Ray, the second Ray, which I have kind of been actual redrawn cure. It will be more like back going to that end. It will basically be a straight line here at the bottom. Um, so pardon that. Uh, So what we have here is a ray going to the to the mirror. Such that Ray going to the mirror such that when it bounces from the mirror you have, though, this diagram does a terrible job of showing you you will have a rare moving parallel to the axis. That is way too. OK, so that's the second Ray here. Uh, let me try to rectify this as much as I can. Okay, so that's supposed to be parallel to the access to the plane or to the access. Then you have raped three drawn on red. And this is the ray passing through the curvature point c. Okay, so there's so It's basically going diagonally from sea to the mirror and then from sea to the image here. And since images inverted image will be on the opposite side, outside as the object. Okay, And then there's Ray for Shown in Green, which intersects, which bounces off this vertex of the mirror and goes to the image shoved to the conversion point all four ways they're converging at this point where the image is but images CPE. That's your ray diagram here on again. Each section 24.3 does a very good job detailing the method for fervor for drawing this out. So that's that's part of it. For part B, we have this equation one over ass, plus one of us prime equals one over f. And so one of us prime the image distance is one of the F minus one over S S O. This is one of 11 minus one of the 16.5, and so this will give us image distance off 33 centimeters. So image eyes 30 centimeters left of the mayor. Okay, And then we'll be going to the next page. Magnification, therefore, is stick to blue. Magnification is negative the image distance as prime over object distance So that negative 33 over 16.5 magnification. Therefore, his negative too. It's magnified twice inverted s So this means that s o. This is of course, equal to ah, white time was a life. So why prime is just negative two times 20.6. Why the image of the object height from the plain So 0.6 millimeters times negative too. So that's negative one for two millimeters. So the image therefore is, uh, 33 centimeters to the left of the mirror and is 1.2 millimeters below the plane. It has a height of 1.2 millimeters below the plane and saw the object is riel hand inverted and that's it.

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