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A spherical mirror produces an image of magnification of $- 1$ on a screen placed at a distance of $50 cm$ from the mirror. The focal length of the mirror is

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25 cm

50 cm

- 25 cm

- 50 cm

answer is C.

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Detailed Solution

The focal length of the mirror is

- 25 cm

.
Given,
Magnification of mirror

(m) = - 1

Image distance

(v) = - 50 cm

Let the distance of the object be

u

The formula of magnification is given as

m = - \frac{v}{u}

\Rightarrow - 1 = - \frac{- 50}{u}

\Rightarrow

u = - 50 cm

Using mirror formula

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

\Rightarrow \frac{1}{f} = \frac{1}{- 50} + \frac{1}{- 50}

\Rightarrow \frac{1}{f} = - \frac{1}{25}

\Rightarrow

f = - 25 cm

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