Question

12. A dedicated sports car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When he looks into one side of the hubcap, he sees an image of his face 30.0 cm in back of it. He then turns the hubcap over, keeping it the same distance from his face. He now sees an image of his face 10.0 cm in back of the hubcap. (a) How far is his face from the hubcap? (b) What is the magnitude of the radius of curvature of the hubcap?

Answer 1

answer) a) we have the mirror equation

1/p+1/q=1/f

p=object distance, q=image distance, f=focal length

here q=negative as the image is forming behind the mirror

so here we have

1/f1=1/f2

1/p-1/30=-1/p+1/10

1/p+1/p=1/30+1/10

2/p=0.1333

p=2/0.1333=15.0 cm

so the answer is 15.0 cm

b) now again using the mirror eqn we have

1/p+1/q=1/f

1/15.0-1/30=1/f

1/f=0.0333

f=1/0.0333

f=30.03 cm

and we know that R=2f=2*30.03=60.0 cm

so the answer is 60.0 cm or 60.1 cm