Question

a concave mirror produces three times enlarged image of an object placed at 10 cm in front of it calculate the radius of curvature of the mirror

Answer 1

Concave mirror, hence enlarged image could mean virtual/ real both

Connotations used-

u is object distance

v is imagine distance

f is focal length

r is radius of curvature

Therefore

m=+-3

Case 1

m=3 Therefore -v/u =3

Therefore v=-3u

Given

u=-10cm

Therefore v=-3u=30cm

As we know ,mirror formula

1/v +1/u = 1/f

Therefore 1/f= 1/-10+ 1/30

By applying mathematical methods

1/f= -2/30

Therefore focal length of mirror is -15cm

Hence..we need not check case 2 since focal length of a concave mirror is always negative..so our case proves right

f=r/2

Therefore

r=2f

Hence r=-30cm

Radius of curvature is -30cm