Concept explainers
It is desired to cast the image of a lamp, magnified 5 times, upon a wall 12 m distant from the lamp. What kind of spherical mirror is required, and what is its position?
The nature of the mirror required and the position of the image when the mirror magnified the image
Answer to Problem 33SP
Solution:
Concave, radius of
Explanation of Solution
Given data:
The distance between thewall and the lampis
The magnification needed by the mirror is
Formula used:
Themirror equation is written as,
Here,
The formula for magnification of the mirror is written as,
Here,
The thin mirror equation is written as,
Here,
Sign convention:
If R is negative, then the centre of curvature is to the left of the mirror, and the mirror is concave.
If R is positive, then the centre of curvature is to the right of the mirror, and the mirror is convex.
If
If
If
If f is positive, then the mirror is concave.
If f is negative, then the mirror is convex.
Explanation:
Recall the expression for themagnification of the mirror.
Understand that the image is formed to the right of the mirror. Hence, the image would be negative and the total distance of image from the mirror will be,
Here,
Substitute
Substitute
Solve for
Understand that the distance of image from the mirror will be the sum of object distance and distance between the wall and the lamp.
Substitute
Recall the expression formirror equation.
Substitute
Solve for
Recall the expression forthin mirror.
Solve for
Substitute
Negative sign indicates that the mirror is concave.
Conclusion:
Therefore, the mirror is c oncave, has a radius of curvature of
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Chapter 36 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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