You are standing 1.52 m in fromt of a large shiny sphere that is 0.675 m in diam

Question

You are standing 1.52 m in fromt of a large shiny sphere that is 0.675 m in diameter.

(a) How far from the surface of the sphere closest to you does your image appear to be? Use a negative number if your image is behind the surface of the sphere and a positive number if your image is in front of the surface of the sphere.
________m
(b) If you are 2.06 m tall, how tall is your image?
________m
(c) Is the image inveted or in the same orientation with respect to you?

o inverted

o same orientation    

o not enough information to tell

Explanation / Answer

1) We can consider, or we must consider the sphere as a convex mirror, then :

1 / p + 1 / q = 1 / f

p = object distance

q = image distance

f = focal distance ; R = 2f

The diameter of the ball is 0.675 cm, then : R = 0.3375 cm

Then : F = .16875 cm

Remember, that for a convex mirror, the focal distance is always negative, then :

1 / 1.52 + 1 / q = - 1 / .16875

q = - 0.1518m

It's a virtual image, as you can see, the sing is negative, and it's 0.1518m, behind the mirror.

If the sign of "q" is negative, then the magnification is positive, we can say then that the image is upright.

2) M = di/d0 = hi/h0
0.1518/1.52 = hi/2.06
hi = 0.2057m

3) same orientation.

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