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ICSE Class 10 Physics 2023 Paper

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Question : 44 of 76
Marks: +1, -0
A convex lens of focal length 10 cm10\ \text{cm} is placed at a distance of 60 cm60\ \text{cm} from a screen. How far from the lens should an object be placed so as to obtain a real image on the screen?
Solution:  
Given: f=+10 cm, v=+60 cm, u=f=+10\ \text{cm},\ v=+60\ \text{cm},\ u= ?
We know,
    1f  =  1v−  1u\;\;\frac{1}{f}\;=\;\frac{1}{v}-\;\frac{1}{u}
∴    1v  =  1f+  1u\therefore\;\;\frac{1}{v}\;=\;\frac{1}{f}+\;\frac{1}{u}
⇒    1+60  =  1+10+  1u\Rightarrow\;\;\frac{1}{+60}\;=\;\frac{1}{+10}+\;\frac{1}{u}
⇒    1u  =  160−  110=  1−660\Rightarrow\;\;\frac{1}{u}\;=\;\frac{1}{60}-\;\frac{1}{10}=\;\frac{1-6}{60}
⇒    1u  =  −560\Rightarrow\;\;\frac{1}{u}\;=\;\frac{-5}{60}
   or     u  =  60−5=−12 cm.\;\text{ or }\;\;u\;=\;\frac{60}{-5}=-12\ \text{cm}.
Thus, the object must be placed at a distance of 12 cm12\ \text{cm} in front of the lens.
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