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Ch 34: Geometric Optics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 34: Geometric OpticsProblem 11b
Chapter 34, Problem 11b

A spherical, concave shaving mirror has a radius of curvature of 32.0 cm. Where is the image? Is the image real or virtual?

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Understand the problem: We are dealing with a spherical, concave mirror with a given radius of curvature. We need to find the position of the image and determine if it is real or virtual.
Recall the mirror equation: The mirror equation relates the object distance (\(d_o\)), the image distance (\(d_i\)), and the focal length (\(f\)) of the mirror. It is given by \(\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}\).
Calculate the focal length: For a spherical mirror, the focal length \(f\) is half the radius of curvature \(R\). Therefore, \(f = \frac{R}{2}\). Given \(R = 32.0\) cm, calculate \(f\).
Determine the image distance: Use the mirror equation to solve for \(d_i\). You will need the object distance \(d_o\) to proceed, which is typically provided in a complete problem statement.
Analyze the nature of the image: If \(d_i\) is positive, the image is real and located on the same side as the object. If \(d_i\) is negative, the image is virtual and located on the opposite side of the mirror.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radius of Curvature

The radius of curvature is the distance from the mirror's surface to its center of curvature. For spherical mirrors, it is twice the focal length. Understanding this helps determine the mirror's focal point, which is crucial for locating the image formed by the mirror.
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Concave Mirror

A concave mirror is a spherical mirror that curves inward, resembling a portion of a sphere. It can form real or virtual images depending on the object's position relative to the focal point. This concept is essential for predicting the nature and position of the image.
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Real vs. Virtual Images

Real images are formed when light rays converge and can be projected onto a screen, while virtual images appear to diverge from a point behind the mirror and cannot be projected. Identifying whether an image is real or virtual involves understanding the mirror's geometry and the object's position.
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Related Practice
Textbook Question

An object 0.600 cm tall is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0 cm. Determine the position, size, orientation, and nature (real or virtual) of the image.

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Textbook Question

Dental Mirror. A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect with a magnification of 2.00 when the mirror is 1.25 cm from a tooth. (Treat this problem as though the object and lie along a straight line.) What must be the focal length and radius of curvature of this mirror?

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Textbook Question

A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. She looks at a penny that is on the bottom of the pool directly below her. To her, the penny appears to be a distance of 7.00 m from her. What is the depth of the water at this point?

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Textbook Question

You hold a spherical salad bowl 60 cm in front of your face with the bottom of the bowl facing you. The bowl is made of polished metal with a 35-cm radius of curvature. Where is the of your 5.0-cm tall nose located?

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Textbook Question

An object is 18.0 cm from the center of a spherical silvered-glass Christmas tree ornament 6.00 cm in diameter. What are the position and magnification of its ?

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Textbook Question

The thin glass shell shown in Fig. E34.15 has a spherical shape with a radius of curvature of 12.0 cm, and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 cm from the center of the mirror along the optic axis, as shown in the figure. Calculate the location and height of the of this seed.

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