Question

A 4.5 Cm Length Of Needle Is Placed Perpendicular To The Principal Axis12 Cm Away From A Convex Mirror Of Focal Length 15 Cm. Give The Magnitude Of Size Of The Image Of The Needle

Answer 1

Given that,

Height of needle = 4.5 cm

Focal length = 15 cm

Object distance = 12 cm

We need to calculate the image distance

Using lens formula

$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$

Where, f = focal length

u = object distance

v = image distance

Put the value into the formula

$\dfrac{1}{15}= \dfrac{1}{v}-\dfrac{1}{12}$

$\dfrac{1}{v}=\dfrac{1}{15}+\dfrac{1}{12}$

$\dfrac{1}{v}=\dfrac{20}{3}$

$v= 6.67\ cm$  

The image distance is 6.67 cm.  

We need to calculate the size of the image of the needle

Using formula of magnification

$m=\dfrac{h'}{h}=-\dfrac{v}{u}$        

Put the value into the formula

$\dfrac{h'}{4.5}=-\dfrac{6.67}{-12}$  

$h'=\dfrac{6.67\times4.5}{12}$

$h'=2.5\ cm$

Hence, The magnitude of size of the image of the needle is 2.5 cm