Answer to Question #37097 in Optics for imran khan

Question

an object is placed 60 cm from a spherical convex mirror. If the mirror forms a virtual image 20cm from the mirror what is the magnitude of the mirror's radius of curvature?

Answer 1

We can find focus coordinate from mirror equation:
1/d_0 + 1/d_i = 1/f

as the the image is virtual, d_i is negative. And we find:
1/f = 1/60 - 1/20 = -2/60 = - 1/30
Hence, focus is at 30 cm from mirror. Focus and radius of curvature are connected as:

R = 2f = 60 cm.