1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Show Light Has The Same Velocity in S and S'

  1. Sep 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the velocity transformation equations. Find the x and y components of the velocity in the frame S of a light ray that has speed c along the y′axis of frame S′ where S and S′are the usual frames we have been considering with S′ moving with speed v with respect to S along the common x − x′ axes. Show that the light ray has speed c in the frame S.

    2. Relevant equations
    1. u'_x = (u_x-v)/{1-(v*u_x/c^2)}
    2. u'_y = u_y/{gamma(1-(v*u_x/c^2))}
    3. u'_z = u_z/{gamma(1-(v*u_x/c^2))}
    3. The attempt at a solution
    u_z = u'_z = 0, obviously. I'm looking for u_x and u_y, so I need to start with u_x. I set u'_x to 0 and solved, getting u_x = v. I'm not sure if that's right, or if I should've gotten c, but I tried to plug u_x = v into equation 2, and did not get that u_y was c.
  2. jcsd
  3. Sep 6, 2012 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Welcome to PF.

    Think about how to get speed from the x and y components of velocity.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook