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A $10 cm$ tall object is placed perpendicular to the principal axis of a convex lens with a focal length of $30 cm$ . The distance of the object from the lens is $20 cm$ . What is the distance of the image?

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+ 20 cm

- 30 cm

+ 40 cm

- 60 cm

answer is D.

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Detailed Solution

The distance of the image is

60 cm

.
Given,
Object distance,

u = - 20 cm

and focal length,

f = + 30 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

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

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

\Rightarrow \frac{1}{v} = \frac{1}{30} + \frac{1}{(- 20)}

\Rightarrow v = - 60 cm

A negative sign indicates that the image will be formed on the same side as that of the object.

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