Magnification equation problem

[Saxby]

Homework Statement

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

Homework Equations

M = -S_i/S
1 / f = (1 / S) + (1 / S_i)

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

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/S_i). From this equation i get S_i=-2, and then plugging S=1 and S_i=-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 :)

 

[ap123]

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

 

[Basic_Physics]

The magnification should be

M = - Si/S

 

[Saxby]

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

 

[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

 

[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).

 

[ap123]

This ray-diagram might be useful in understanding the situation
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/mirray.html
(bottom image)

 

[Saxby]

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