Question

18. An object 2 cm tall is placed on the axis of a convex lens of focal length 5 cm at a distance of 10 m from the
optical centre of the lens. Find the nature, position and size of the image formed. Which case of image
formation by convex lenses is illustrated by this example ?
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Answer 1

GIVEN :

• Height of a object on the axis of a convex lens, h1 = 2 cm.
• Focal length = 5 cm.
• Distance, u = - 10 m = - 1000 cm.

TO FIND :

• The nature of the image formed.
• The position of the image formed.
• The size of the image formed.

SOLUTION :

$\large \sf \leadsto \dfrac {1}{f} \ = \ \dfrac {1}{v} \ - {1}{u}$

Put the values in the above formula.

$\implies \sf \dfrac {1}{v} \ - \ \dfrac {1}{-1000} \ = \ \dfrac {1}{5}$

$\implies \sf \dfrac {1}{v} \ = \ \dfrac {1}{5} \ - \ \dfrac {1}{-1000}$

$\implies \sf \dfrac {(200-1)}{-1000}$

$\qquad \large {\underline {\boxed {\sf V \ = \ 5.02 \ cm}}}$

•°• Therefore, The image is formed behind 5.02 cm convex lens and image is formed inverted and real.

$\large \leadsto \sf m \ = \ \dfrac {v}{u}$

$\implies \sf m \ = \ \dfrac {5.02}{-1000}$

$\implies \sf m \ = \ \dfrac {h_2}{h_1} \ = \ -0.005$

$\implies \sf \dfrac {h_2}{2} \ = \ -0.005$

$\qquad \large {\underline {\boxed {\sf h_2 \ = \ -0.01 \ cm}}}$

•°• Therefore, The example illustrate the case that object is at infinity. The object distance is greater than its focal length.