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A screen is placed $100 \mathrm{~cm}$ from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20 \mathrm{~cm}$. The focal length of the lens is
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The correct answer is:
$24 \mathrm{~cm}$
Given, distance between screen and object, $d=100 \mathrm{~cm}$
Separation between the two pośitions of convex lens, $\quad x=20 \mathrm{~cm}$
focal length of the lens, $f=\frac{d^2-x^2}{4 d}$
$$
\begin{aligned}
& =\frac{(100)^2-(20)^2}{4 \times 100} \\
& =\frac{10000-400}{400}=\frac{9600}{400} \\
& =24 \mathrm{~cm}
\end{aligned}
$$
Separation between the two pośitions of convex lens, $\quad x=20 \mathrm{~cm}$
focal length of the lens, $f=\frac{d^2-x^2}{4 d}$
$$
\begin{aligned}
& =\frac{(100)^2-(20)^2}{4 \times 100} \\
& =\frac{10000-400}{400}=\frac{9600}{400} \\
& =24 \mathrm{~cm}
\end{aligned}
$$
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