Question

Please help

A dedicated sports-car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When she looks into one side of the hubcap, she sees an image of her face 25.0 cm in back of the hubcap. She then flips the hubcap over and sees another image of her face 10.0 cm in hack of the huhcap. (a) How far is her face from the hubcap? (b) What is the radlus of curvature of the hubcap?

Answer 1

Using curved mirror equations u as object distance, v as image distance and f as focal length

for first case

1/v - 1/u = 1/f
1/25 - 1/u = 1/f

for second case

1/v + 1/u = 1/f
1/10 + 1/u = 1/f

equating both we get

1/10 - 1/u = 1/25 + 1/u

1/10 - 1/25 = 2/u

u = 33.33 cm

put in 1 to get f

f = 7.69 cm
but R = 2f = 15.38cm