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If the distance of the object from the concave mirror is $4$ times the focal length, then the position of the image will be obtained at

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v = \frac{f}{5}

v = \frac{5 f}{4}

v = \frac{- 4 f}{3}

v = \frac{2 f}{5}

answer is C.

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Detailed Solution

If the distance of the object from the concave mirror is

4

times the focal length, then the position of the image will be obtained at

v = \frac{- 4 f}{3}

.
Given,
The distance of the object from the concave mirror is 4 times the focal length, that is

u = - 4 f

Focal length,

f = - f

(concave mirror)
Using mirror formula, we get

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

\Rightarrow \frac{1}{- f} = \frac{1}{- 4 f} + \frac{1}{v}

\Rightarrow \frac{1}{v} = \frac{1}{4 f} - \frac{1}{f}

\Rightarrow \frac{1}{v} = \frac{- 3}{4 f}

\Rightarrow v = \frac{- 4 f}{3}

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