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Question

Object is placed on the principal axis of a concave mirror. Its real image is formed at a point which is 10 cm more distant from the mirror than the object. If focal length of mirror 12 cm. The magnitude of magnification of the image is:

A
1
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B
2.5
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C
1.5
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D
2
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Solution

The correct option is C 1.5
Given:
Focal length, f=12 cm
Object distance =u
Image distance (v) is 10 cm more than the object distance v=(u+10). Real images for concave mirrors are formed on the same side as the object for concave mirrors.
Using mirror formula,
1u+1v=1f
1u+1(u+10)=112
Simplifying,
u214u120=0
u220u+6u120=0
(u20)(u+6)=0
Object distance is taken as u. Hence, u is positive.
u=20 cm
Hence, image distance is:
v=30 cm
Magnification is given by:
m=Image DistanceObject Distance
m=3020=1.5
Magnitude of magnification is:
|m|=1.5

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