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Finding magnification, object distance from the mirror, and radius of curvature

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data
    You placed a 10cm high object in front of a mirror and got 5cm high virtual image at (-30cm). (Hint: watch the sign convention)
    a. Find the magnification
    b. Find the object distance from the mirror
    c. Find the radius of curvature of the mirror

    then I have to know if the mirror is convex or concave and if it is upright or inverted, but I think I can figure that out if I find the solutions to these problems.


    2. Relevant equations
    I've figured out from the information that Ho= 10cm, Hi= 5cm, I think f= -30cm
    For object distance, I can't figure out how I can possibly figure that out without any distances given. I'm not supplied with distance from focal point.
    Any ideas on what I'm doing wrong?

    and for radius, I have no idea where to begin.

    3. The attempt at a solution
    for part a. M=Hi/Ho=5cm/10cm=1/2cm ? So does Magnitude equal 1/2cm?

    I am not good at science, I am taking this as my gen-ed required science for my major. PLEASE help however you can.
    Thanks so much :-)
     
  2. jcsd
  3. Apr 12, 2012 #2
    Hello,

    let s= object distance=x, s'=image distance=-30cm, h= object height=10cm, h'=image height=5cm, f=focal length=y and R=Radius of curvature=z

    For part A you have the right answer as m=-[itex]\frac{s'}{s}[/itex] Except you thought -30 is focal length which it is not, its where the image appears to be.

    For part B you can use the following equation [itex]\frac{1}{f}[/itex]=[itex]\frac{1}{s}[/itex]+[itex]\frac{1}{s'}[/itex]. You don't know object distance but you can work it out from magnification equation, m=-[itex]\frac{s'}{s}[/itex] we also know |m|=[itex]\frac{h'}{h}[/itex] so you can work out what s is.

    For part C Radius of curvature is simply 2x Focal length.

    Hope this helps
     
  4. Apr 12, 2012 #3
    that helps so much! thank you!
     
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