A dedicated sports-car enthusiast polishes the inside and outside surfaces of a

Question

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 31.0 cm behind the hubcap. He then turns the hubcap over and sees another image of his face 9.9 cm behind the hubcap.

(a) How far is his face from the hubcap?
cm
(b) What is the radius of curvature for the hubcap?
cm
(c) What is the magnification for each image?

(d) Are the images virtual or real?

(e) Are the images upright or inverted?

Explanation / Answer

given;
s1' = -31 cm
s2' = -9.9 cm

event #1

2/R = 1/s + 1/s1'

2/R = 1/s + 1/(-31).................(1)


event #2

-2/R = 1/s + 1/s2'

-2/R = 1/s + 1/(-9.9).................(2)

eqn (1) - eqn (2)

4/R = 1/14.54

R = 58.16 cm

from eqn (1)

2/R = 1/s + 1/(-31)

s = 15.004 cm


ans:
(a) the face is 15.004 cm far from hubcap
(b) radius of hubcap is 58.16 cm

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