Question

Convex mirror has a focal length of 20cn. Determine an object location for which the Image will be one half the size of the object

Answer 1

Answer :

The object location is 20cm in front of the mirror.

Given :

• A convex mirror has a focal length of 20cm
• The image size is one half the size of the object

To Find :

• The location of the object i.e. object distance

Formulae to be used :

Mirror formula :

$\sf \star \: \: \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$

Formulafor magnification of mirror :

$\sf \star \: \: m =\dfrac{h_{2}}{h_{1}} =-\dfrac{v}{u}=\dfrac{f}{f-u}=\dfrac{f-v}{f}$

Solution :

We have ,

focal length, f = 20cm

Image size is half of object size ,

⇒h₂ = (1/2)h₁

⇒ h₁ = 2h₂

where h₁ is object size

and h₂ is image size

Appying magnification formula we have :

$\sf \implies m = \dfrac{h_{2}}{h_{1}} = \dfrac{f}{f-u} \\\\ \sf \implies \dfrac{h_{2}}{2h_{2}} = \dfrac{20}{20- u } \\\\ \sf \implies \dfrac {1}{2}=\dfrac{20}{20 - u }\\\\ \sf \implies 20 - u = 40\\\\ \sf \implies -u = 40 - 20 \\\\ \sf \implies -u = 20 \\\\ \sf \implies u = -20cm$

Object location is 20cm in front if the mirror.