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A concave mirror produces three times enlarged virtual image of an object placed at 10 cm in front of it. Calculate the radius of curvature of the mirror.
Distance of the object from the mirror $u$ = $-$10 cm
Magnification, $m$ = 3
To find: Focal length $(f)$, and the radius of curvature $(R)$.
From the magnification formula, we know that-
Substituting the given values in the magnification formula we get-
Thus, the distance of the image, $v$ is 30 cm from the mirror, and the positive sign implies that the image forms behind the mirror (on the right).
Now, from the mirror formula, we know that-
Substituting the given values in the mirror formula we get-
Thus, the focal length, $f$ of the mirror is 15 cm.
We know that the radius of curvature, $R$ is equal to twice the focal length $f$ of the mirror.
Hence, the radius of curvature of the mirror is 30 cm.
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