Question

size of image of an object by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd to its size. At what distance the object has been placed from the mirror? what is the nature of the image and the mirror?.

Answer 1

here consider two cases of possible spherical mirrors.
for concave mirror:
F=-20cm u=? v=? m=-1/3
m=-v/u =-1/3⇒ v=u/3
1/v+1/u=1/f⇒1/u/3+1/u=1/f
3/u+1/u=1/f⇒4/u=1/-20
∴u=-80cm

for convex mirror:
m=+1/3 f=+20
m=-v/u=+1/3⇒v=-u/3
1/v+1/u=1/f
1/-u/3=1/u=1/f⇒-3/u+1/u=1/f⇒-2/u=1/+20
∴u=-2×20=-40cm