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Question

A person looks into a spherical mirror. The size of the image of his face is twice the actual size of his face. If the face is at a distance of 20 cm from the mirror, then the nature and radius of curvature of the mirror is

A
Concave, 80 cm
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B
Concave, 40 cm
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C
Convex, 80 cm
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D
Convex, 40 cm
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Solution

The correct option is A Concave, 80 cm
Given:
m=+2
[ as a person is able to see image of his face, so the image is virtual]
u=20 cm
So, m=ffu
+2=ff(20)
On solving this, we get,
f=40 cm
As focal length is negative, the mirror is concave.
Now, radius of curvature of the mirror,
|R|=2|f|=80 cm

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