Question

# An object is placed at a distance of $$30\ cm$$ from a concave mirror of focal length $$20\ cm$$, then nature and magnification of the image will be:

A
Real,2
B
Apparent,2
C
Real,+2
D
Apparent,+2

Solution

## The correct option is A $$\text{Real}, -2$$Given,focal length, $$f = -20 \,cm$$image distance, $$u = -30 \,cm$$object distance, $$v = ?$$Using mirror formula,$$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$$$$\dfrac{1}{v} + \dfrac{1}{-30} = \dfrac{1}{-20}$$or $$\dfrac{1}{v} = -\dfrac{1}{20} + \dfrac{1}{30} = \dfrac{-3 + 2}{60} = -\dfrac{1}{60}$$$$\therefore v = -60\,cm$$ (real image)$$\therefore$$ Magnification, $$m = -\dfrac{v}{u} = -\dfrac{-60}{-30} = -2$$or $$m = -2$$Physics

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