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A convex lens of focal length 30cm forms a real image three times larger than the object on a screen. Object and screen are moved until the image becomes twice the size of object. If shift of the object is 6cm. The shift of screen is 7(x)cm. Find the value of (x).

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answer is 4.

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Detailed Solution

$\frac{1}{3 x} - \frac{1}{(- x)} = \frac{1}{30} \Rightarrow x = 40 cm So, 3 x = 120 cm$

To decrease the magnification object should be moved towards 2F₁ , image moved towards 2F₂.
Let displacement of image is y.
$\begin{array}{l} 2 (40 + 6) = (120 - y) \\ y = 28 \Rightarrow 7 (x) \\ x = 4 \end{array}$

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