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$\cdot$ A 3.80 -mm-tall object is 24.0 $\mathrm{cm}$ from the center of a sil-vered spherical glass Christmas tree ornament 6.00 $\mathrm{cm}$ indiameter, What are the position and height of its image?

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1.6 cm0,25 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

Simon Fraser University

University of Sheffield

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.

05:55

A 3.80-mm-tall object is $…

03:03

An object is 24.0 $\mathrm…

04:24

An object is 18.0 cm from …

05:12

01:38

06:05

01:11

An object is $15.0 \mathr…

03:25

A 3.0 -cm-tall object is $…

01:24

An object $4.50 \mathrm{~c…

02:54

02:46

A certain Christmas tree o…

03:44

04:31

A converging meniscus lens…

Okay. The equation we use is is this one of her image distance? Plus, whenever one of our object distance was one of the image distances, they go to one of her folk elect. Remember, focal length is 1/2 of the rays of curvature. So that's two over our now we were given a diameter of the glass and that's of the glass mayor, not six centimetres. So half the diameter is a radius. So are will be three centimeters, but it will be a negative two centimetre. Since this is ah is a convex. The mirror surfaces is a convex lens. So s O to find as prime we just pull as to the other one of us to their side. So we get one of us prima's to over negative three centimeters miners one over 21 centimeter. Then I know 24 centimeters is given in the book as the um distance from the center of the mirror. So therefore object itself is placed 24 minus two radius just three. So that's 21 centimeters from the center, 21 centimeters from the mirror on dso. So when we get here is that as prime is, Ah, negative 1.4 centimeters. This means it's a virtual image because time is a much distance of negative and so image. Therefore, image is ah, three minus one point for so 1.6 centimeters from from the center. And so so we needed to subtract the three from the night of 1.4 because because because that's the way it's a culture of the smear servants. We want to know where the images from from center on. Dso images on the same side. Ah, same side of the lens as object. Great hons. And so we have image distance so we to find image. Height is a magnification formula is negative. Es primero es so that's negative. Negative equals positive, 1.4 centimeters over 21. So that's 0.667 on DH. So that is also equal to y primary. Why, therefore, why prime is equal to point 0667? This is a positive times. Why just objects height? And that's 3.8 millimeters. So the image the height of the image turns out to be 0.25 three millimeters

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