Find the radius of curvature of the mirror

Question

A magnifying mirror produces an erect virtual image 2.5 times as high as the object 24 cm from it. Find the radius of curvature of the mirror.

Answer 1

p = 24 cm

 

1/f = -2/R

 

1/f = 1/p + 1/q = -2/R

 

M = -p/q = 2.5

 

q = -p/M = -24 cm / 2.5 = -9.6 cm

 

-2/R = 1/p + 1/q = (1/24 - 1/9.6) cm^-1 = -0.0625 cm^-1

 

R = -2 / (-0.0625) cm = 32 cm