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