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  • A convex lens of focal length forms a real image three times larger than the object on

A convex lens of focal length \mathrm{30\ cm} 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 the object. If the shift of the object is \mathrm{6\ cm}. The shift of screen is:

Option: 1

\mathrm{28\ cm}


Option: 2

\mathrm{14\ cm}


Option: 3

\mathrm{18\ cm}


Option: 4

\mathrm{16\ cm}


Answers (1)

best_answer

\mathrm{We\ have,\ \frac{1}{3 x}-\frac{1}{(-x)}=\frac{1}{+30}}\\ \mathrm{\therefore \quad x=40 \mathrm{~cm}\ and\ \quad 3 x=120 \mathrm{~cm}}

To decrease the magnification object should be moved towards \mathrm{2f_{1}}.
Hence, image will move towards \mathrm{2f_{2}} .Let displacement is \mathrm{y}.
Then, 

\mathrm{\begin{aligned} & 2(40+6)=(120-\mathrm{y}) \quad\left(\because \mathrm{m}=\frac{\mathrm{v}}{\mathrm{u}}\right) \\ \therefore \quad \mathrm{y}= & 28 \mathrm{~cm} \end{aligned}}

 

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