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The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is________ cm.

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Detailed Solution

$\begin{array}{l} We know for Lens, \\ m = \frac{f}{f + u} \\ Case 1: - m = \frac{f}{f + u_{1}} \\ Case 2 : + m = \frac{f}{f + u_{2}} \end{array}$

$\begin{array}{l} Equating both \\ \Rightarrow - (\frac{f}{f + u_{1}}) = (\frac{f}{f + u_{2}}) \\ \Rightarrow - (f + u_{1}) = (f + u_{2}) \\ \Rightarrow - (f - 20) = (f - 10) \\ \Rightarrow - f + 20 = f - 10 \\ \Rightarrow 2 f = 30 \\ \Rightarrow f = \frac{30}{2} = 15 cm \end{array}$

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