Question

A 5cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20cm. the distance of the object from the lens is 30cm. Find the (i) position (ii) nature (iii) size of the image formed
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Answer 1

${\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}}$

• $\:\sf{h_{o}= 5cm }$

• $\:\sf{u = -30cm }$

• $\:\sf{f= 20cm }$

${\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}}$

• $\:\sf{v \:= \:? }$

• $\:\sf{h_{i} \: = \: ?}$

${\mathfrak{\underline{\purple{\:\:\: Solution:-\:\:\:}}}}$

⠀${\sf{ Using \ lens \ formula \ \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} }}$⠀⠀⠀⠀⠀

${\mathrm{\underline{\:\:We\:have\:\:}}}$

$\dashrightarrow\:\: \sf{\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}}$

$\dashrightarrow\:\: \sf{\dfrac{1}{20} + \dfrac{1}{-30}=\dfrac{1}{60}}$

$\dashrightarrow \:\:\sf{ v = 60cm}$

$\star\:\sf{Magnification\:\dfrac{v}{u}=\dfrac{60}{-30}=-2}$

${\boxed{\rm{\blue{Magnification\:=\:\dfrac{Image\:size}{Object\:size}}}}}$

$\dashrightarrow\:\: \sf{\dfrac{h_{i}}{h_{o} = -2}}$

$\dashrightarrow\:\: \sf{\dfrac{h_{i}}{5}= -2}$

$\dashrightarrow\:\: \sf{ h_{i} = -2\times 5}$

$\sf{\dashrightarrow\:\: {h_{i} = -10cm}}$

${\green{\checkmark}}\:\sf\underline{The\:image\:is\:real\: inverted\:and\: magnified}$