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Chapter 16: Problem 62

You hold a shiny tablespoon at arm's length and look at the concave front side of the spoon. (a) Is the image you see of yourself upright or inverted? (b) Is the image enlarged or reduced? (c) Is the image real or virtual?

Short Answer

Expert verified
(a) Inverted, (b) Enlarged, (c) Virtual.

Step by step solution

01

Understanding Concave Mirrors

A concave surface, like the front side of a shiny spoon, behaves as a concave mirror. The nature of the image formed by a concave mirror depends on the object's position relative to the mirror's focal point and center of curvature.
02

Analyzing Image Characteristics

When you look into a concave mirror at arm's length, you are typically within its focal point. If the object is between the mirror and the focal point, the image formed is: (a) inverted, (b) enlarged, and (c) virtual.
03

Conclusion from Concave Mirror Principles

In the case of the spoon, (a) the image is inverted because of the mirror's properties, (b) the image appears enlarged, and (c) because it cannot be projected onto a screen, the image is virtual.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Image Characteristics
When we talk about image characteristics in the context of concave mirrors, we focus on a few key aspects: orientation, size, and type of image. A concave mirror can form images that are either upright or inverted, and their size could be enlarged, reduced, or actual-size.

  • **Orientation**: The orientation of the image depends on where the object is located relative to the mirror's focal point. When an object is within the focal length of a concave mirror, the image tends to be upright. However, if the object is beyond the focal point, the image is inverted.
  • **Size**: The size of the image also changes with the object's distance from the mirror. Inside the focal point, the image appears larger. Outside of it, the image can either be reduced or appear magnified, depending on the distance.
  • **Type**: Finally, whether an image is real or virtual depends on whether it can be projected. If an image can be displayed on a screen, it's real; if it cannot, it's virtual.
Understanding these characteristics is crucial when studying the behavior of light and optics, especially in applications involving lenses and mirrors.
Virtual Image
A virtual image is one that appears to be in a location from which light does not actually come. This is in contrast to a real image, which is formed by light converging at a focal point.

In the case of concave mirrors, virtual images are typically formed when an object is placed between the mirror and its focal point. This creates images that appear behind the mirror. Key features of virtual images are:
  • **Non-invertible**: These images usually appear upright rather than inverted.
  • **Non-projectable**: Virtual images cannot be projected onto a screen because they are not made from actual light converging.
  • **Magnification**: Often, virtual images appear larger than the actual object in a concave mirror setup.
These images are common in everyday experiences, such as looking at oneself in a spoon or makeup mirror.
Focal Point
The focal point of a concave mirror is a specific position where parallel light rays converge after reflecting off the mirror. The behavior of light in relation to the focal point determines the types of images the mirror can produce.

For a concave mirror:
  • **Position**: It is located along the principal axis, some distance in front of the mirror. This distance is called the focal length.
  • **Image Formation**: If an object is placed right at the focal point, no image is formed on a straightforward projection, as the light rays run parallel after reflecting.
  • **Beyond and Within the Focal Point**: Beyond the focal point, concave mirrors produce real and inverted images. But within it, they generate virtual, upright, and often enlarged images.
Understanding the focal point is essential for predicting image formation in various setups involving concave mirrors. It also helps in designing optical devices where image orientation and size are critical considerations.

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Most popular questions from this chapter

Hale Telescope The \(5.08-\mathrm{m}\)-diameter concave mirror of the Hale Telescope on Mount Palomar has a focal length of \(16.9 \mathrm{~m}\). An astronomer stands \(20.0 \mathrm{~m}\) in front of this mirror. (a) Where is her image located? Is it in front of or behind the mirror? (b) Is her image real or virtual? How do you know? (c) What is the magnification of her image?

You view a nearby tree in a concave mirror. The inverted image of the tree is \(3.5 \mathrm{~cm}\) high and is located \(7.0 \mathrm{~cm}\) in front of the mirror. If the tree is \(21 \mathrm{~m}\) from the mirror, what is its height?

Diagram Two plane mirrors meet at right angles at the origin of a coordinate system, as shown in Figure 16.17. A long object extends from \(x=1 \mathrm{~m}\) and \(y=1 \mathrm{~m}\) to \(x=4 \mathrm{~m}\) and \(y=2 \mathrm{~m}\). Draw all three of the images formed by the two mirrors. (Hint: One of the three images is due to reflections from both mirrors.)

A boy sees his reflection in a reflecting globe \(0.55 \mathrm{~m}\) away in a garden. If the reflecting globe has a diameter of \(45 \mathrm{~cm}\) and the boy is \(1.7 \mathrm{~m}\) tall, what is the height of his image in the globe?

Think \& Calculate Standing \(2.0 \mathrm{~m}\) in front of a very small mirror, you see the reflection of your belt buckle, which is \(0.70 \mathrm{~m}\) below your eyes. (a) What is the vertical location of the mirror relative to the level of your eyes? (b) What angle do your eyes make with the horizontal when you look at the buckle? (c) If you now move backward until you are \(6.0 \mathrm{~m}\) from the mirror, will you still see the buckle, or will you see a point on your body that is above or below the buckle? Explain.
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