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Chapter 32: Problem 50

What kinds of images, virtual or real, are formed by a converging mirror when the object is placed a distance away from the mirror that is a) beyond the center of curvature of the mirror, b) between the center of curvature and half the center of curvature, and c) closer than half of the center of curvature.

Short Answer

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Short Answer: When the object is placed (a) beyond the center of curvature, the converging mirror forms a real, inverted, and smaller image; (b) between the center of curvature and half the center of curvature, the mirror forms a real, inverted, and enlarged image; and (c) closer than half of the center of curvature, it forms a virtual, upright, and enlarged image.

Step by step solution

01

Case a: Object beyond the center of curvature of the mirror

When the object is placed at a distance beyond the center of curvature (C) of the mirror, the converging mirror forms a real, inverted, and smaller image between the center of curvature and the focal point (F) of the mirror. The image is formed by converging the reflected light rays.
02

Case b: Object between the center of curvature and half the center of curvature

In this case, when the object is placed between the center of curvature (C) and half the center of curvature (i.e., the focal point (F)), the converging mirror forms a real, inverted, and enlarged image beyond the center of curvature. The image is formed by converging the reflected light rays.
03

Case c: Object closer than half of the center of curvature

When the object is placed closer than half the center of curvature (i.e., closer than the focal point (F)), the converging mirror forms a virtual, upright, and enlarged image behind the mirror. The image is formed by extending the reflected light rays backward, and the image appears to be on the same side as the object.

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Most popular questions from this chapter

Even the best mirrors absorb or transmit some of the light incident on them. The highest-quality mirrors might reflect \(99.997 \%\) of incident light intensity. Suppose a cubical "room, \(3.00 \mathrm{~m}\) on an edge, were constructed with such mirrors for the walls, floor, and ceiling. How slowly would such a room get dark? Estimate the time required for the intensity of light in such a room to fall to \(1.00 \%\) of its initial value after the only light source in the room is switched off.

You are under water in a pond and look up at the smooth surface of the water, noticing the sun in the sky. Is the sun in fact higher in the sky than it appears to you while under water, or is it lower?

A solar furnace uses a large parabolic mirror (mirrors several stories high have been constructed) to focus the light of the Sun to heat a target. A large solar furnace can melt metals. Is it possible to attain temperatures exceeding \(6000 \mathrm{~K}\) (the temperature of the photo sphere of the Sun) in a solar furnace? How, or why not?

What is the magnification for a plane mirror? a) +1 c) greater than +1 b) -1 d) not defined for a plane mirror

Among the instruments Apollo astronauts left on the Moon were reflectors used to bounce laser beams back to Earth. These made it possible to measure the distance from the Earth to the Moon with unprecedented precision (uncertainties of a few centimeters out of \(384,000 \mathrm{~km}\) ), for the study both of celestial mechanics and of plate tectonics on Earth. The reflectors consisted not of ordinary mirrors, but of arrays of corner cubes, each consisting of three square plane mirrors fixed perpendicular to each other, as adjacent faces of a cube. Why? Explain the function and advantages of this design.
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