A rod of length 2l is at rest in frame O' with co-ords (x',y',z')=(±l,λ,0)(adsbygoogle = window.adsbygoogle || []).push({});

Observer O moves at speed u along the x axis.

The first part of the question is just to derive the length contraction - fine, O measures the length as 2l / γ

The next part has me stuck:

"Show that, at t = 0, the observer O sees the light rays from the two ends of the rod

coming in at angles that lead to an apparent length of 2lγ (making the assumption

that the rod is oriented parallel to the x-axis with a y separation of λ from the origin).

Comment briefly on the discrepancy between the two results. "

I've tried drawing space-time diagrams, and just got in a bit of a mess. I can work out equations for the worldlines of the front and back of the pole (e.g. for one end (ct,x,y,z) = (ct'γ - lγ u/c, γ t'-lγ ,λ,0) etc), but setting t=0 for front and back just gives the 2l / γ. result

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# Homework Help: Length Contraction

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