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  • The distance between an object and the screen is 100cm. A lens placed between them produces an image on the screen when the lens is placed at two positions 40cm apart. The power of the lens is near

The distance between an object and the screen is 100cm. A lens placed between them produces an image on the screen when the lens is placed at two positions 40cm apart. The power of the lens is nearly: 

Option: 1

3 diopters


Option: 2

5 diopters


Option: 3

2 diopters


Option: 4

9 diopters


Answers (1)

best_answer

At first position of lens, let the distance of lens from object and screen be u and v respectively.


\mathrm{\therefore \quad x+y=100}

\mathrm{\therefore }  At second position of lens the distance of lens from object and screen shall be v and u respectively.

\mathrm{\therefore \mathrm{y}-\mathrm{x}=40 }

Solving equation (1) and (2) we get
\mathrm{ y=70 \mathrm{~cm}=\frac{70}{100}=\mathrm{m} \text { and } x=30 \mathrm{~cm}=\frac{30}{100}=\mathrm{m} }

\mathrm{ \therefore \quad } The power of lens is,  \mathrm{ P=\frac{1}{f}=\frac{1}{y}+\frac{1}{x}=\frac{100}{70}+\left(\frac{100}{30}\right)=\frac{100}{21} \approx 5 } diopters.

Posted by

Ritika Kankaria

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