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  • The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is 40cm. The area of the image is 9 times that of the square.

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is 40cm. The area of the image is 9 times that of the square. The focal length of the lens is : 

Option: 1

36cm\, \: \: \:


Option: 2

27\: cm


Option: 3

60\: cm


Option: 4

30\: cm


Answers (1)

best_answer

 if side of object square  =?

 and side of image square  =?′

 From question, 

(\frac{\ell}{\ell})^2 =9 \ \ or

 

\\ \frac{\ell^{\prime}}{\ell}=3\\ \\ \text { i.e., magnification } m=3 u=-40 cm \\ \\ v=3 \times 40=120 cm \ \ \ then, f =?

\\ \begin{aligned} &\frac{1}{v}-\frac{1}{u}=\frac{1}{f} \frac{1}{120}-\frac{1}{-40}=\frac{1}{f}\\ &\frac{1}{f}=\frac{1}{120}+\frac{1}{40}=\frac{1+3}{120} \\ \therefore f=30 cm \end{aligned}

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Gaurav

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