Question

An object 8 cm high is placed at a distance of 24 cm from a convex mirror of radius of curvature 36 cm. The size of
the image formed is _____cm.

1. 8.4

2.24.4

3.3.43

4 .14.14​

Answer 1

I have to explain in possible way

Answer 2

Given :

➳ Height of object = 8cm

➳ Distance of object = 24cm

➳ Radius of curvature = 36cm

(Focal length = 36/2 = 18cm)

➳ Type mirror : convex

To Find :

➝ Height of image.

SoluTion :

✴ Distance of image :

$:\implies\rm\:\dfrac{1}{u}+\dfrac{1}{v}=\dfrac{1}{f}$

$:\implies\rm\:\dfrac{1}{(-24)}+\dfrac{1}{v}=\dfrac{1}{18}$

$:\implies\rm\:\dfrac{1}{v}=\dfrac{1}{18}+\dfrac{1}{24}$

$:\implies\rm\:\dfrac{1}{v}=\dfrac{7}{72}$

$:\implies\bf\:v=10.28\:cm$

✴ Height of image :

$:\implies\rm\:m= -\dfrac{v}{u}=\dfrac{h_i}{h_o}$

$:\implies\rm\: -\dfrac{10.28}{(-24)}=\dfrac{h_i}{8}$

$:\implies\rm\:h_i=0.428\times 8$

$:\implies\underline{\boxed{\bf{ h_i=3.43\:cm}}}$