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Optics: Speed of the Image

  1. Nov 21, 2012 #1
    1. The problem statement, all variables and given/known data

    An object is placed 20cm from a converging lens of focal length 5cm. If the object moves towards the lens at a speed of 12cm/s, at what speed does the image move away from the lens?

    2. Relevant equations

    1/f=1/di+1/do
    v=d/t
    3. The attempt at a solution
    Let's say the object moves...
    Do=do1+do2
    Di=di2-di1
    so if di+fdo/do-f
    vt=(fdo2/do2-f)-(fdo1/do1-f)
    However, both vi and ti are unknown, so how should I proceed?
     
  2. jcsd
  3. Nov 21, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Hi Lara, welcome to PF.

    Have you studied some Calculus? The object moves towards the lens so the object distance is do=20-12t in terms of time. The velocity of the object is d(do)/dt=-12 cm/s. The velocity of the image is vi=d(di)/dt. In the lens equation, both do and di are functions of the time. Find the derivative of di at time t=0 when do = 20 cm.

    ehild
     
  4. Nov 22, 2012 #3
    Thank you for your help!
     
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