Question

an object of size 5cm is palced at a distance of 25cm from the pole of concave mirror of radius curvature 30 cm. calculate the position and size of the image so formed . what will be the nature of image​

Answer 1

Given :

Height of object = 5cm

Distance of object = 25cm

Radius of curvature = 30cm

Type of mirror : concave

To Find :

Position, nature and size of the image.

Solution :

❖ Focal length of concave mirror is taken negative and that of convex mirror is taken positive.

Distance of image can be calculated by using mirror formula which is given by

$\dag\:\underline{\boxed{\bf{\purple{\dfrac{1}{u}+\dfrac{1}{v}=\dfrac{1}{f}}}}}$

We know that, f = R/2

• f = 30/2 = 15 cm

$\sf:\implies\:\dfrac{1}{(-25)}+\dfrac{1}{v}=\dfrac{1}{(-15)}$

$\sf:\implies\:\dfrac{1}{v}=-\dfrac{1}{15}+\dfrac{1}{25}$

$\sf:\implies\:\dfrac{1}{v}=\dfrac{-5+3}{75}$

$\sf:\implies\:v=-\dfrac{75}{2}$

$:\implies\:\underline{\boxed{\bf{\orange{v=-37.5\:cm}}}}$

♦ Size of the image :

➙ m = -v / u = h' / h

• h' denotes height of image
• h denotes height of object

➙ -(-37.5)/(-25) = h'/5

➙ h' = -37.5/5

➙ h' = -7.5 cm

♦ Nature of image :

• Real
• Inverted
• Enlarged