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The concave lens’ focal length is $15 cm$ , and the image distance is $10 cm$ , then the object distance is ____ $cm$ .

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Detailed Solution

The concave lens’ focal length is

15 cm,

and the image distance is

10 cm,

then the object distance is

30 cm

.
A concave lens of focal length

f = - 15 cm

and image distance

v = - 10 cm

(as the image formed is always to the left of the concave lens) is given.
By lens formula,

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

Where

f

u

and

v

are the focal length, object distance and image distance, respectively.

\Rightarrow \frac{1}{- 15} = \frac{1}{- 10} - \frac{1}{u}

\Rightarrow \frac{1}{u} = \frac{1}{15} - \frac{1}{10}

\Rightarrow \frac{1}{u} = \frac{2 - 3}{30} = \frac{- 1}{30}

\Rightarrow u = - 30 cm

Hence, the object distance is

30 cm

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