Image Distance and Magnification

[erik-the-red]

Question

An object is a distance of 23.4 cm from the center of a silvered spherical glass Christmas tree ornament which has a diameter of 5.70 cm.

A What is the position of its image?

B What is the magnification of its image?

I think the object can be treated as a convex mirror.

s (object distance) = 23.4 cm
R = -(5.70)/2 = -2.85 cm

\frac{1}{s} + \frac{1}{s'} = \frac{2}{R}

Using that equation, I get \frac{1}{s'} = \frac{2}{-2.85} - \frac{1}{23.4}.

Then, s' = -1.12 cm.

And, m = -\frac{s'}{s}, so m = .048.

I know for sure that -1.12 cm is not the correct answer, so most likely my second answer is also incorrect.

What did I do wrong?

 

[erik-the-red]

Did I not provide enough work?

 

[Doc Al]

Your method is fine but check your arithmetic.

 

[erik-the-red]

Sorry, I still get the same answer.

 

[Doc Al]

Using that equation, I get \frac{1}{s'} = \frac{2}{-2.85} - \frac{1}{23.4}.

Then, s' = -1.12 cm.

Please redo this calculation.

 

[erik-the-red]

Doc Al,

Indeed, it was incorrect. Thanks!