Question

A concave mirror forms a real image of an object

placed in front of it at a distance 30 cm, of size three

times the size of object. Find (a) the focal length

of mirror (b) position of image

Answer 1

according to sign convention, in concave mirror,
u(distance of object from mirror)=-30 cm
as image is three times bigger than the object, magnification (m)=+3
m=-v/u, (v=distance of image from mirror)
+3= -v/-30
3= v/30
v=90 cm
focal length (f)
1/f = 1/v + 1/u
1/f = 1/90 + (1/-30)
1/f = 1/90 - 1/30
1/f = (1-3)/90
1/f = -2/90
1/f = -1/45
f = -45 cm
focal length is 45 cm
and image is 90 cm from the mirror.