Past exam of the physics 1 paper of the University of Oxford / 2016 / 7

For a Lorentz boost along $x$, the Lorentz transformation isTo calculate a photograph, compare photons that arrive together, which were generally emitted at different times. Put the lamina in the $xy$ plane, moving along $+x$, and take the distant camera to lie along negative $y$. Let $(X,Y)$ be a material point's coordinates in the lamina's rest frame. At a laboratory time $t$, its position satisfies $x=X/\gamma +vt$, $y=Y$.

The distant-camera approximation makes the variable part of the light travel time $Y/c$. Equal arrival time therefore requires $t+Y/c=\text{constant}$. Choose that constant to be zero. The point's photographed transverse coordinate becomesA stationary lamina rotated in its plane by $\theta$ would instead have the projected coordinate $X\cos \theta -Y\sin \theta$. The two projections agree whenThis is Terrell rotation. The shape defined by simultaneous laboratory positions still has length contraction; the photographic rotation comes from combining that contraction with unequal emission times. Reversing the viewing or motion direction reverses the apparent rotation's sign.