Concept explainers
The radius of curvature of the mirror.
Answer to Problem 28SSC
The radius of curvature of the mirror is 29 cm .
Explanation of Solution
Given:
The height of the object is ho=6.0 cm .
The position of the object is do=16.4 cm .
The height of the image is hi=2.8 cm .
Formula used:
The expression for the mirror equation is,
1do+1di=1f
Here, do is the position of the object, di is the position of the image, and f is the focal length.
The expression for the magnification equation is,
m=hiho=−dido
Here, hi is the height of the image and ho is the height of the object.
The expression for the radius of curvature is,
r=2|f|
Calculation:
The position of the image is,
m=hiho=−didodi=−hidohodi=−(2.8 cm)(16.4 cm)(6.0 cm)di=−7.7 cm
The focal length is,
1do+1di=1ff=dodidi+dof=(16.4 cm)(−7.7 cm)(−7.7 cm)+(16.4 cm)f=−14.5 cm
The radius of curvature of the mirror is,
r=2|f|r=2|(−14.5 cm)|r=29 cm
Conclusion:
Thus, the radius of curvature of the mirror is 29 cm .
Chapter 17 Solutions
Glencoe Physics: Principles and Problems, Student Edition
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