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An object of a height of $6 cm$ is placed perpendicular to the principal axis of a concave lens of a focal length of $5 cm$ , and the distance of the object from the lens is $10 cm$ . What is the distance of the image formed?

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- 2.66 cm

- 3.33 cm

- 4 cm

- 6 cm

answer is B.

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Detailed Solution

The distance of the image formed is

- 3.33 cm

.
Given,
Object distance,

u = - 10 cm

and focal length,

f = - 5 cm

.
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}{(- 5)} + \frac{1}{(- 10)}

\Rightarrow \frac{1}{v} = \frac{- 2 - 1}{10}

\Rightarrow v = - 3.33 cm

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

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