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An object is placed at a distance of $6 cm$ from a convex mirror of focal length $12 cm$ . Find the nature of the image.

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Real and inverted

Virtual and erect

Both

1

and

2

None of the above

answer is B.

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Detailed Solution

An object is placed at a distance of

6 cm

from a convex mirror of focal length

12 cm

. The nature of the image is virtual and erect.
Given that,

u = - 6 cm

f = + 12 cm

(positive: as the mirror is convex)

v = ?

By applying the mirror formula,

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

\Rightarrow

\frac{1}{12} = \frac{1}{v} + \frac{1}{- 6}

\Rightarrow \frac{1}{12} = \frac{(6 - v)}{6 v}

\Rightarrow 6 v = 72 - 12 v

\Rightarrow 18 v = 72

\Rightarrow v = + \frac{72}{18} cm

\Rightarrow v = + 4 cm

+ ve

sign indicates that the image will be formed

4 cm

behind the mirror and since the image is formed behind the convex mirror, it would be virtual and erect.

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