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To form a real image on the wall, how far from the convex lens the object has to be placed if the focal length of it is $10 cm$ placed at a distance of $12 cm$ from a wall?

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30 cm

55 cm

120 m

60 cm

answer is D.

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Detailed Solution

The object distance must be

60 cm

.
Given,
Image distance,

v = + 12 cm

[Positive: as the wall is in opposite side of the object]
Focal length,

f = + 10 cm

[Positive: as the lens is convex]
Form the lens formula,

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

Where

f

v

, and

u

are the focal length, image distance and object distance, respectively.
On arranging the terms, we get

\Rightarrow \frac{1}{u} = \frac{1}{v} - \frac{1}{f}

On substituting the given values, we get the object distance as

\Rightarrow \frac{1}{u} = \frac{1}{12} - \frac{1}{10}

\Rightarrow \frac{1}{u} = \frac{(5 - {6)}_{}}{60}

\Rightarrow u = - 60 cm

Hence, the object has to be placed at a distance of

60 cm

in front of the lens.

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