Finding Object Distance for Upright Image with Magnification +1.51 for Concave Mirror

[longcatislong]

Homework Statement

Suppose the radius of curvature of a concave mirror is 5.0 cm
a) Find the object distance that gives an upright image with a magnification of +1.51.

Homework Equations

1/Do + 1/Di= 1/f

m=-di/do=hi/ho

The Attempt at a Solution

First i convered all cm into m.

f=R/2, so .05/2 = .025.
1/.025=40

then I used m=-Di/Do. Since don't know Do or Di, I substituted for the unknowns using 1/Do + 1/Di= 1/f

I came up with...
m=-[40-(1/Do)]/[40-1/(40-1/Do)] and solved for Do.

I got Do=.02506m.

Online HW says it's wrong.

Any help is GREATLY appreciated. What I did makes sense to me but obviously there's an error or just some major concept I don't understand. Thank you so much for taking the time!

 

[collinsmark]

Homework Statement

Suppose the radius of curvature of a concave mirror is 5.0 cm
a) Find the object distance that gives an upright image with a magnification of +1.51.

Homework Equations

1/Do + 1/Di= 1/f

m=-di/do=hi/ho

The Attempt at a Solution

First i convered all cm into m.

f=R/2, so .05/2 = .025.

Okay, everything seems right so far.

1/.025=40

I'm not sure why you would want to invert that at this point in the process, but okay.

then I used m=-Di/Do. Since don't know Do or Di, I substituted for the unknowns using 1/Do + 1/Di= 1/f

Substitution is the right idea.

I came up with...
m=-[40-(1/Do)]/[40-1/(40-1/Do)] and solved for Do.

Now you've lost me.

So far, you've already figured out
[tex] \frac{1}{D_o} + \frac{1}{D_i} = \frac{1}{f} [/tex]
and
[tex] m = -\frac{D_i}{D_o}. [/tex]
Rather than going the other way around, try substituting [itex] D_i = -mD_0 [/itex] into the first equation. Also substitute [itex] f = R/2 [/itex] into the first equation. It might make it a little easier to solve for [itex] D_o [/itex] that way. (Hint: then find a common denominator for the left side of the equation )

 

[longcatislong]

Oh god that's SO much simpler than what I was trying to do. Thanks a million!

 

[Redbelly98]

Glad it worked out. By the way, I find it easier to work in cm rather than meters for this problem. For example, "1/2.5" is easier (for me) to work with than "1/0.025". In the end you get the same answer, of course.

 

[asteriatic]

Your solution seems to be on the right track. It is possible that there is a small calculation error in your final answer. You may want to double check your calculations and try rounding to a different number of significant figures to see if that helps. Additionally, make sure you are using the correct sign convention for the magnification (positive for upright images). If you are still having trouble, it may be helpful to break down the problem into smaller steps and check each step individually. It is also a good idea to ask a classmate or your instructor for help if you are still stuck. Keep up the good work!