Spherical Mirror and Object Distance

[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 = - d_i/d_o. 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/d_o + 1/d_i = 1/F, I rearranged to get
d_o + d_i = F and since F = .12,
d_o = .12 - d_i

I solved for d_i using M = - d_i/d_o with M = 2, so
2 = - d_i/d_o rearraged to,
d_i = - 2d_o

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

Solving gives: d_o = - .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.

 

[ehild]

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?

Yes.

I'm having trouble finding the object's distance too. I know that M = - d_i/d_o. 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/d_o + 1/d_i = 1/F, I rearranged to get
d_o + d_i = F

This is wrong. Try again.

Solving gives: d_o = - .12 m

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


ehild

 

[Skye77]

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

 

[ehild]

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

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

ehild

 

[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

:(

 

[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

 

[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!