radius of curvature for a convex mirror

Question

It is desired that a convex mirror produce a magnification of 0.21 when an object is placed 32 cm from the mirror. What radius of curvature must the mirror have?

Answer 1

M = 0.21

x_o = 32 cm

M = x_i / x_o

∴ x_i = M · x_o = (0.21) · (32 cm) = 6.7 cm

1 / x_i + 1 / x_o = 1 / f

∴ f = ( x_i x_o) / ( x_i + x_o ) = 5.5 cm

R = 2 f = 11 cm