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Question

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

A
2.0
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B
1.5
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C
0.67
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D
2.5
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Solution

The correct option is B 1.5
Since the mirror is concave, focal length is f=12 cm
Let u be the object distance and v be image distance.

Using mirror formula,
1u+1v=112(i)

Given, image is 10 cm more left than the object. Image distance is:
v=u10(ii)

Substituting (ii) in (i), we get:
1u+1u10=112
u10+u(u10)u=112
Simplifying, we get
u2+14u120=0
u={20 cm, 6 cm}

Object distance cannot be positive.
u=20 cm

Image distance is:
v=u10=30 cm

Magnification is given by:
m=vu
m=(30)20
m=1.5

Magnitude of magnification is:
|m|=1.5

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