Question

A 5 cm 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 30 cm determine the size of the image formed *

+60cm
+10cm
-60cm
-10cm​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• Height of object = 5cm

• Focal length, f = +20

• Object distance, u= -30

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Size of image

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

$\underline{\:\textsf{Using lens formula :}}$

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

$\dashrightarrow \sf \dfrac{1}{20}= \dfrac{1}{v}-\dfrac{1}{-30}\\ \\ \dashrightarrow \sf \dfrac{1}{20}+\dfrac{1}{-30}= \dfrac{1}{v}\\ \\ \dashrightarrow \sf \dfrac{1}{20}-\dfrac{1}{30}= \dfrac{1}{v}\\ \\ \dashrightarrow \sf \dfrac{3-2}{60}=\dfrac{1}{v}\\ \\ \dashrightarrow \sf \dfrac{1}{60}=\dfrac{1}{v}\\ \\ \ \dashrightarrow \boxed{\sf{\green{v = 60cm}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Again,

$\underline{\:\textsf{We know that :}}$

$\dashrightarrow \sf \dfrac{v}{u}= \dfrac{h_i}{h_o}$

$\underline{\:\textsf{Putting the given values :}}$

$\dashrightarrow \sf \cancel{\dfrac{60}{-30}}= \dfrac{h_i}{5}\\ \\ \dashrightarrow \sf -2\times 5= h_i\\ \\ \dashrightarrow \sf -10= h_i\\ \\ \dashrightarrow \boxed{\sf{\green{h_i = -10cm}}}$

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ Size of image is </p><p>\textbf{-10cm}}}.$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\boldsymbol{\: Option\:D)\: is \: correct√}$

Answer 2

D is the correct option ❔