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Question

A man holds a spherical shaving mirror of radius of curvature 60 cm, and focal length 30 cm, at a distance of 15 cm, from his nose. Find the position of image, and calculate the magnification.

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Solution

Distance of the object, i.e. nose, from the mirror (u) = -15 cm
The focal length of the concave mirror (f) = -30 cm
We have to find the distance of the image (v).
Using the mirror formula, we get
1f=1v+1u

1-30=1v-115
or 1v=115-130or 1v=2-130or 1v=130 v=30 cm
Thus, the position of the image is 30 cm behind the mirror.
Now, using the magnification formula, we get
m=-vu
m=-30-15=2
Therefore, the image is 2 times magnified than the object.

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