An object is kept at a distance of 4cm from the first focus of a convex lens. A real image is formed at a distance of 9cm from its second focus. Then focal length of that lens is

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13 cm

36 cm

6 cm

6.5 cm

answer is C.

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Detailed Solution

Given that

${OF}_{1} = 4 cm {IF}_{2} = 9 cm$

$u = - (4 + f) v = (f + 9)$

We can have lens formula

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

$\Rightarrow \frac{1}{9 + f} + \frac{1}{4 + f} = \frac{1}{f}$

$\Rightarrow \frac{(4 + f + 9 + f)}{(9 + f) (4 + f)} = \frac{1}{f}$

$\Rightarrow (13 + 2 f) f = 36 + 13 f + f^{2}$

$\Rightarrow 13 f + 2 f^{2} = 36 + 13 f + f^{2}$

$\begin{aligned} \Rightarrow f^{2} = 36 \\ ∴ f = 6 cm \end{aligned}$

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