- #1

- 10

- 0

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.

- What's the time (Δt) measure by O for the photon to make a full period.

2. 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.

So for 1, the answer is [itex] \Delta t= \dfrac{2l}{c} [/itex]. I tried to do 2 too, but I keep getting a somewhat incorrect answer. Here's what I do:

Draw an isosceles triangle [itex]ABC[/itex] with [itex] |AB| = vt' [/itex], and the height is l. I figured that [itex] t' = \dfrac{2|AB|}{c'} [/itex], where [itex] c' = c-v [/itex]. So we try to solve the following equation: [itex] (c't')^2 = 4l^2 + (vt')^2 [/itex], but if I solve for t', I get an almost correct answer, which of course is still incorrect. You get [itex] t' = \dfrac{2l}{\sqrt{c^2-2cv}} [/itex], and of course we want [itex] t= \dfrac{2l}{c} [/itex] because in newtonian mechanics t=t'. What have I done wrong?