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  • An object of height 4.0 cm is placed at a distance of 30 cm from the optical centre ‘O’ of a convex lens of focal length 20 cm. Draw a ray diagram to find the position and size of the image formed. Mark optical centre ‘O’ and pr

An object of height 4.0 cm is placed at a distance of 30 cm from the optical centre ‘O’ of a convex lens of focal length 20 cm. Draw a ray diagram to find the position and size of the image formed. Mark optical centre ‘O’ and principal focus ‘F’ on them diagram. Also find the approximate ratio of size of the image to the size of the object.

 

 

 

 
 
 
 
 

Answers (1)

Object distance \mathrm{u}=-30 \mathrm{cm}$
Focal length of convex lens $\mathrm{f}=20 \mathrm{cm}$ 
\mathrm{Height}$ of object $\mathrm{h}_{\mathrm{o}}=4 \mathrm{cm}$
Using lens formula :
\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ \\ $\therefore \frac{1}{\mathrm{v}}-\frac{1}{-30}=\frac{1}{20}$

\begin{aligned} &\Longrightarrow \mathbf{v}=60 \mathrm{cm}\\ &\text { Magnification } \frac{\mathrm{h}_{\mathrm{i}}}{\mathrm{h}_{\mathrm{o}}}=\frac{\mathrm{v}}{\mathrm{u}}\\ &\Longrightarrow \frac{h_{i}}{4}=\frac{60}{-30}\\ &\Longrightarrow \mathrm{h}_{\mathrm{i}}=-8 \mathrm{cm}\\ &\text { Ratio of size of image to that of object }=\frac{\left|\mathrm{h}_{\mathrm{i}}\right|}{\left|\mathrm{h}_{\mathrm{o}}\right|}=\frac{8}{4}=2 \end{aligned}

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Satyajeet Kumar

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