 Solution

Use emission, reflection and return-to-source events $A,B,C$. In the source-and-mirror rest frame their $(ct,x)$ coordinates are $A=(0,0)$, $B=(d,d)$ and $C=(2d,0)$. The laser and mirror have vertical worldlines; the two light rays have slopes $\pm 1$ on a diagram with equal spatial and $ct$ scales.

For a frame moving with velocity $+v$ along the outgoing beam, let $\beta =v/c$ and $\gamma =(1-{\beta }^2{)}^{-1/2}$. A Lorentz transformation givesBoth laser and mirror now move towards negative $x^{\prime }$, with worldlines $x^{\prime }=-v{t}^{\prime }$ and $x^{\prime }=d/\gamma -v{t}^{\prime }$. Light still has slopes $\pm 1$. The moving observer's own worldline is $x^{\prime }=0$; it should not be confused with the moving source worldline.