Past exam of the physics 1 paper of the University of Oxford / 2014 / 5 / b

Take the light to travel along positive x, while the water moves with signed velocity $-v$. In the water's rest frame its light phase velocity is $c/n$. The relativistic velocity addition law from a gives the laboratory phase velocityExpanding to first order in $v/c$, with $nv/c\ll 1$, yieldsEquivalently $w\simeq c/n-v(1-1/n^2)$: the counterflow reduces the forward light speed. This is the nondispersive Fresnel drag coefficient. The refractive index is taken as constant over the relevant frequencies; dispersion and its frequency-shift corrections are outside this approximation.