An image of candle on a screen is found to be double its size. When the candle is shifted by a distance of 5 cm then the image becomes triple it size. Find the nature and radius of curvature of the mirror?

Dear Student,
1/f=1/di1 - 1/do1------1
1/f=1/di2-1/do2-------2

m=-di/do
=>2=di1/do1
=>di1=2do1

m=-di2/do2
=>3=di2/do1+5
=>di2=3do1+15
1
1/f=1/2do1 -1/do1
=>f=-2/do1

2
-do1/2 = 1/3do1+15 + 1/do1+5
=>do1=-0.6 or -4.39

f=3.33cm or 0.455cm
R=6.66cm or 0.91cm

as focal length is positive hence the mirror is concave mirror.