Question

A concave mirror has a focal length of 4 cm and an object 2 cm tall is placed 9 cm away from it. Find the nature, position and size of the image formed.

Answer 1

focal length = f = - 4cm
height of object = + 2cm
object distance = u = - 9cm
image distance = v = ?
height of image = size = h' = ?

mirror formula,

1/v + 1/u = 1/f

1/v = 1/f - 1/u
= -1/4 - (-1/9)
= -1/4 + 1/9
= -9 + 4/36
= -5/36

v = 36/-5
= -7.2 cm

Hence,
the image is formed at a distance of 7.2 cm from the mirror.

Magnification = m

m = -v/u
= -(-7.2)/-9
= -0.8

As the magnification is negative , the image is real , inverted.


also,

m = h'/h
-0.8 = h'/2
h' = -1.6 cm

SIZE OF THE IMAGE IS 1.6 CM