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Light clock - Galilean transformations

  1. Sep 21, 2014 #1
    We have two parallel mirrors, which are located at y=0 and y=l in the (x,y) plane. A photon is travelling between the mirrors, up and down along the y-axis. Consider an observer O at rest w.r.t. the mirrors.

    1. What's the time (Δt) measure by O for the photon to make a full period.
    Consider an observer O' which moves along the x-axis with a speed v, which is constant. Assume l' = l.

    1. Using Galilean transformations from Newt. mech. , what's the time measured by O' for the photon to make a full period (draw a picture to illustrate the logic). Compare this with the time measured by O.

    2. Now use the postulate that c=c'. Compute the period Δt' again and compare it to Δt, writing it as Δt' = γΔt, for some value of γ. Check γ>1. Interpret the results.
    So for 1, the answer is Δt=2l/c. But I don't know how to do 2 (and as a result of that, 3). I don't know what to draw and the Galilean transformation eludes me. First I thought that you had to draw a triangle, with sides of 0.5vt, l and ct/2. But that accomplishes nothing. Can I get some help please.
     
  2. jcsd
  3. Sep 21, 2014 #2

    Simon Bridge

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    Do you have some notes about the galilean transformations?
    Remember that for the second set, the speed of light is not c, but c'.
    Apart from that the reasoning is fine... only you are asked for a full period, which would be an isoceles triangle.
    Consider: what is the height of the triangle from base to apex?
     
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