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  • (i) A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate the focal length of the lens used. (ii) A co

(i) A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate the focal length of the lens used.

(ii) A converging lens is kept coaxially in contact with a diverging lens- both the lenses being of equal focal length. What is the focal length of the combination?

 

 

 

 
 
 
 
 

Answers (1)

The final image is formed on the screen.

For location 1

\frac{1}{f}=\frac{1}{y}-\frac{1}{-x}\; \; \; \; \; \; \; ----(1)

For location 2

\frac{1}{f}=\frac{1}{y-20}-\frac{1}{-(x+20)}\; \; \; \; \; \; \; ----(2)

From (1) and (2)

\frac{1}{y}+\frac{1}{x}=\frac{1}{y-20}+\frac{1}{x+20}

\frac{x-y}{xy}=\frac{(x-y)}{(y-20)(x+20)}

xy=(y-20)(x+20)

xy=xy-20x+20y-400

x-y=-20

Also x+y=100

\therefore x=40

    y=60

\frac{1}{f}=\frac{1}{60}-\frac{1}{40}\Rightarrow f=24\; cm

ii)  the focal length of the combination

\frac{1}{f}=\frac{1}{f}+\frac{1}{-f}

\Rightarrow f=\infty

Posted by

Safeer PP

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