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An object is placed $50 cm$ from a mirror that produces a virtual image at a distance of $10 cm$ behind the mirror. Which of the following are the nature and focal length of a mirror?

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Concave mirror and

f = + 12.5 cm

Convex mirror and

f = + 12.5 cm

Convex mirror and

f = - 12.5 cm

Concave mirror and

f = - 12.5 cm

answer is B.

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Detailed Solution

If the object is placed

50 cm

from a mirror that produces a virtual image at a distance of

10 cm

behind the mirror, then the mirror would be a convex mirror and its focal length

f = + 12.5

.
As it was given that the virtual image formed behind the mirror, then the mirror used would be a convex mirror.
Given,
Object distance,

u = - 50 cm

Image distance,

v = 10 cm

By mirror formula, the relation between the focal length

(f)

, image distance

(v)

and object distance

(u)

is given as

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

Substituting the value of

u

and

v

, we get

\Rightarrow \frac{1}{10} + \frac{1}{(- 50)} = \frac{1}{f}

\Rightarrow \frac{(- 50) + 10}{10 \times (- 50)} = \frac{1}{f}

\Rightarrow \frac{1}{f} = \frac{- 40}{- 500}

\Rightarrow f = \frac{- 500}{- 40}

\Rightarrow f = + 12.5

Thus, the focal length of the mirror with the given details is

+ 12.5 cm

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