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A $4.5 cm$ needle is placed $12 cm$ away from a convex mirror of a focal length of $15 cm$ . What is the magnification of the image?

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- 0.2

+ 0.5

+ 0.67

+ 0.56

answer is D.

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Detailed Solution

The magnification of the image is

+ 0.56

Given,
Needle distance from the mirror,

u = - 12 cm

Focal length of the mirror,

f = + 15 cm

Using mirror formula

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

\Rightarrow \frac{1}{15} = \frac{1}{- 12} + \frac{1}{v}

\Rightarrow

\frac{1}{v} = \frac{1}{15} + \frac{1}{12}

\Rightarrow

\frac{1}{v} = \frac{3}{20}

\Rightarrow

v = + \frac{20}{3}

cm
The formula of magnification is given as

m = - \frac{v}{u}

\Rightarrow m = - \frac{20 / 3}{- 12}

\Rightarrow m \approx + 0.56

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