An object is held at the principal focus of a concave lens of focal length f. The image will be formed between centre and its .

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Detailed Solution

An object is held at the principal focus of a concave lens of focal length

f .

The image will be formed between the optical centre and its focus.
The lens formula for a concave lens is given by

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

We can write it as

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

Given that the object is placed at focus, then the object distance is

u = f

Focal length

- f

and object distance

- u

is negative for a concave lens.
Therefore,

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

\Rightarrow

v = - \frac{f}{2}

Thus, the image will be formed between the optical centre and focus of the lens; towards the side of the object.

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