# Spherical Mirror and Object Distance

1. Nov 4, 2009

### Skye77

If a spherical mirror has a radius of curvature of .24 m and and object is placed in front of it and magnified to twice its size: is the mirror concave, convex, or either? And what is the object's distance?

I determined that the mirror was concave, because the question said that the image was twice the object's size and convex mirrors decrease image size. Is this correct?

I'm having trouble finding the object's distance too. I know that M = - di/do. And M will either = 2 or -2 because the image could be real or virtual.

From the question I got that R = .24 and since F = R/2, F = .12
Then, using the equation 1/do + 1/di = 1/F, I rearranged to get
do + di = F and since F = .12,
do = .12 - di

I solved for di using M = - di/do with M = 2, so
2 = - di/do rearraged to,
di = - 2do

Plugging this to the spherical-mirror equation gave me: do = .12 - (- 2do)

Solving gives: do = - .12 m

Is this correct? Am I going about this the right way, or am I way off base? Any help is appreciated. Thank you.

2. Nov 4, 2009

### ehild

Yes.

This is wrong. Try again.

The object is in front of the mirror, its distance should be positive. But you are quite near to the right way .

ehild

3. Nov 4, 2009

### Skye77

So then am I only off because of the negative sign? So the answer would be .12 m

4. Nov 4, 2009

### ehild

No, you made a mistake saying that di +do =F.

ehild

5. Nov 4, 2009

### Skye77

I got that equation from my book and I've tried rearranging it several times and I still get the same answer. What am I missing?

1/do + 1/di = 1/F

M= - di/do and since M = -2 I get di = 2do

Then I plug that into the equation and still get .12

:(

6. Nov 4, 2009

### ehild

di=M*do

1/do+1/(Mdo) =1/F

factor out do:

(1/do)*(1+1/M)=1/F

do=F*(1+1/M)

M is either 2 or -2., F=0.12 m.

Plug in.

ehild

7. Nov 4, 2009

### Skye77

Thanks for all the help. I just realized when I was doing my math I was making the same bone-head mistake over and over again.

Must get more sleep to avoid stupid mistakes!