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$\cdot$ Repeat the previous problem, except use a convex mirror with the same magnitude of focal length.

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a) 3.75 $\mathrm{cm}$, 2 $\mathrm{mm}$b) 3.33 $\mathrm{cm}$, 2.66 $\mathrm{mm}$c) 1.67 $\mathrm{cm}$, 1.34 $\mathrm{mm}$d) 4.97 $\mathrm{cm}$, 3.98 $\mathrm{mm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

Hope College

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.

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11:22

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01:33

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All right. We're given a convex mirror here. Falling also probably five, which was a con Kemer. So for Ah convex mirror, you have our coverage. Radius of curvature of mirror is less than zero gsr were negative are meaning that r and here is negative 10 senators. We're also given that why the height also object is eight millimeters our 0.8 centimeters. So for parts aid through D, we have to find the image Height are at least first the object the same image distance as prime then the image height y prime. And this implicitly means you have to find magnification. Okay, so well, two equations here. So for image distance, we have one over object distance plus no plus one over image distance equals to over are the biggest curvature. And then for magnification you have magnification equals negative image Does distance over object distance. Which is he called to image height over object height. All right, so let's get started. Part air were given. That s object distance is 15 centimeters. So this means that as's prime will be related by this equation. So one over 15 plus one over X prime will be equal to negative to over 10. These are all in centimeters and there's a negative there because our is negative. 10. So it's pulling out that negative signs. This means that one of rest time will be equal to negative to over 10 minus one over 15. And you work that out and take the reciprocal of the right hand side and you get that s prime is negative. 3.75 centimetres. So 3.75 centimeters on the opposite side of the mirror as the objectives. So from them from the magnification equation, then we have that magnification. His minus X prime over s is just 3.75 There's a negative on B s prime, but so negative before it, which cancels out the negatives and the quantity over 15 again, both centimeters. This gives you one forts or 2.25 and finally we have that. It's just right. It just right over here we have that This is also equal to why trying over why and so why is eight millimeters? So why prime is one forts times eight equals two millimeters. That's the height of the image. And of course, because Why? Privates? Positive. This is upright image. Okay on. So we follow the same the same methodology for all the other problems for all the other parts. And I'm going to do each with a different think So for part B were given, that s is 10 centimeters. This implies that one arrest prime is again two of our which is negative to over 10 minus one over 10. And so as prime is negative 3.33 centimeters, it means that em is negative. 2.23 are negative. Negative positive 2.33 over 10 and so magnification as 1/3. Which means that why prime is 1/3 times eight. So that's 2.67 millimeters of camp moving on to the next page part. See, you have that as is 2.5 centimeters. So this implies that as prime when you put that in this equation with our 10 is negative one point 67 centimeters. So this means that magnification is 1.61 point 675 and so that's 2/3. This means that why prime 2/3 times eight threats 5.33 millimeters and Finally, we have party where ass is 10 millimeter, 10 meters on one meter is 100 centimetres or 10 times 100 calls 1,000 centimeters. So in this case, will have won over asses. Prime equals negative to over 10 again minus one over 1,000. This gives us as prime as negative. 4.98 Um, centimeters for M is 4.98 over 1,000 just 1,000 and self. This gives us a magnification of 4.98 times 10 to the negative three very not very magnified. And so why, prime will be, uh, this, um Right here times eight millimeters. And so that's 0.0 for millimeters. And notice that white trying it's positive for all of these. Answer is meaning that apologies images are upright.

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