What is the mirror's focal length?

[jaejoon89]

A concave mirror creates an image on the screen 2x larger than the object. Both objects and screen are subsequently moved in order to create an image on the screen 3x larger than the object. 1) If the screen is moved 0.75 m in this process, how far is the object also moved? 2) What is the mirror's focal length?

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I think the equations are:
1) M = h_i / h_o = - d_i / d_o
2) 1/f = 1/d_o + 1/d_i
where i refers to image, o refers to object

I'm really not sure how to set this up.

 

[Delphi51]

You could try putting the given information into the two formulas.
Repeat for the situation after moving the screen and object.
Looks like 4 equations and 4 unknowns, so you should be able to find anything you want!

 

[nlightner]

Can you provide more information about the setup and the values of the variables? Are we assuming the object is at the focal point of the mirror at the beginning? Also, are we assuming the mirror is a perfect concave mirror with no distortion? This information will help me provide a more accurate response.