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A convex lens produces a twice as large real image when an object is placed at a distance of 18 cm from it. Where should the object be placed to produce a thrice as large real image?

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44 cm

- 16 cm

- 12 cm

21 cm

answer is B.

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Detailed Solution

To get a thrice as large real image, the object must be placed at

16 cm

in front of the lens.
It has been given that,
Object distance,

(u) = - 18 cm

Magnification,

m = \frac{v}{u}

= - 2

(since image is real and hence inverted)

- v = 2 \times (- 18)

\Rightarrow v = 36 cm

Using lens formula,

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

\Rightarrow f = \frac{36}{3}

\Rightarrow f = 12 cm

For a real image thrice as large, magnification

m = - 3

\Rightarrow m = \frac{v}{u}

v = - 3 u

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

\Rightarrow \frac{1}{f} = \frac{1}{- 3 u} - \frac{1}{u}

\Rightarrow \frac{1}{12} = \frac{- 4}{3 u}

\Rightarrow u = \frac{- 4 \times 12}{3}

\Rightarrow u = - 16 cm

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