A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is \( -3 \), then the magnitude of the radius of curvature of the mirror is:
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For concave mirrors, use the mirror equation \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \), and the magnification to solve for unknown distances or focal lengths.
The magnification \( m \) is calculated as:
\[
m = -\frac{v}{u}
\]
Here, \( v \) represents the image distance and \( u \) represents the object distance. The mirror equation is also provided:
\[
\frac{1}{f} = \frac{1}{v} + \frac{1}{u}
\]
Given the magnification and the relationship between focal length \( f \) and radius of curvature \( R \):
\[
f = \frac{R}{2}
\]
Solving these equations yields a radius of curvature \( R = 15 \, \text{cm} \).
