A 2cm high object is placed 7.1cm from concave mirror whose radius of curvature is 10.2cm. Find the value of image distance.
Answers
Given: Height of the object = 2cm
Object distance or the distance between the object and mirror (u)=7.1cm
The Radius of curvature of concave mirror= 10.2 cm
To find: Image distance or the distance of the image from the mirror(v)
Solution: Focal length of the concave mirror (f) = 2R
f=2R
f=2x10.2
f=20.4cm
Focal length of concave mirror will be positive for a concave mirror i.e. +20.4cm
The mirror formula = 1/f =1/u + 1/v
= 1/20.4=1/7.1+1/v
=1/20.4=1v+7.1/7.1v
cross multiplying
7.1v =20.4(1v+7.1)
7.1v=20.4v+144.84
7.1v-20.4v=144.84
-13.33v=144.84
v= -10.86cm
The image distance is -10.86cm which means that the image is formed in front of the mirror.