Homework Help: Magnification equation problem

1. Feb 11, 2013

Saxby

1. The problem statement, all variables and given/known data
When an object is closer to a concave mirror than the mirror's focal point the...
(a) Magnification is more than 1
(b) Magnification is less than 1

2. Relevant equations
M = -Si/S
1 / f = (1 / S) + (1 / Si)

M = Magnification
S = Distance between object and mirror
Si = Distance between image and mirror
f = Distance between focal point and mirror

3. The attempt at a solution
I an attempt to solve this problem i simply plugged in values where S<f, in this case i'll use S=1 and f=2.

Plugging these values into the second equation i receive: 1/2 = (1/1) + (1/Si). From this equation i get Si=-2, and then plugging S=1 and Si=-2 into the second equation i get: M = -(-2/1) which is M = 2.

If M=2 this leads me to believe that the answer to this question is (a), but according to the answers provided it should be (b). I really can't figure out where I've made a mistake. Any help would be much appreciated :)

Last edited: Feb 11, 2013
2. Feb 11, 2013

ap123

Yes, I think (a) is correct.
Try drawing a principal-ray diagram to convince yourself.

3. Feb 11, 2013

Basic_Physics

The magnification should be

M = - Si/S

4. Feb 11, 2013

Saxby

Sorry, i believe i wrote that the wrong way round but i used M = -Si/S in my solution

5. Feb 11, 2013

Saxby

I've edited it now, but i still have the same problem in that the answer i have isn't the same as the answer provided

Last edited: Feb 11, 2013
6. Feb 11, 2013

Basic_Physics

Concave mirrors are used to shave or put on makeup since they produce virtual (Si negative and thus on the other side of the mirror) enlarged upright images as you found by a positive (upright image) larger than 1 (enlarged) magnification (image larger than object).

7. Feb 11, 2013

ap123

8. Feb 13, 2013

Saxby

Ok, turns out my answer was right. Thanks for your help everyone :)