Concept explainers
A spherical concave mirror has a radius of curvature of -400 cm. An object 2.00 cm tall is on the central axis 400 cm in front of the mirror. (a) Determine the focal length. (b) Locate the image. (c) Describe the image. (d) Determine the magnification. [Hint: Check out Fig. 36-5.]
(a)
The focal length of a
Answer to Problem 26SP
Solution:
Explanation of Solution
Given data:
The radius of curvature is
The height of the object is
The distance of the object from the concave mirror is
Formula used:
The thin mirror equation is written as,
Here,
Sign convention:
If R is negative, the centre of curvature is to the left of the mirror, and the mirror is concave.
If R is positive, the centre of curvature is to the right of the mirror, and the mirror is convex.
If f is positive, the mirror is concave.
If f is negative, the mirror is convex.
Explanation:
Recall the expression forthin mirror.
Solve for
Substitute
The positive sign indicates that the mirror is concave.
Conclusion:
Therefore, the focal length of the mirror is
(b)
The location of the image, when a
Answer to Problem 26SP
Solution:
The real image is
Explanation of Solution
Given data:
The radius of curvature is
The height of the object is
The distance of the object from the concave mirror is
From previous part, the focal length of the given concave mirror is
Formula used:
The thin mirror equation is written as,
Here,
Sign convention:
If
If
If
If f is positive, the mirror is concave.
If f is negative, the mirror is convex.
Explanation:
Consider the expression forthinmirror.
Understand that the object is placed at a distance of
Substitute
Solve for
The positive sign indicates that the image is real.
Conclusion:
Therefore, the location of t hereal image is
(c)
The nature of the image, when a
Answer to Problem 26SP
Solution:
The image is r eal, inverted, and of the same size as the object.
Explanation of Solution
Introduction:
From table 36-1 in the textbook, it is clear that when the object is at a distance of
Explanation:
Draw the diagram ofa concave mirror when the object is placed at a distance of
From the above figure, it is clear that when the object is placed at a distance of
Conclusion:
Therefore, the image formed by the concave mirror is real, inverted , and of the same size as the object.
(d)
The magnification, when a
Answer to Problem 26SP
Solution:
Explanation of Solution
Given data:
The radius of curvature is
The height of the object is
The distance of the object from the concave mirror is
From part (a), the focal length of the given concave mirror is
Formula used:
The formula for the magnification of the mirror is:
Here,
Explanation:
Consider the expression for the magnification of the mirror.
Obtain the value of
Substitute
The negative sign indicates that the image is inverted.
Conclusion:
Therefore, the magnification is
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Chapter 36 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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