 Prism sweep under different rotation conventions

For a prism in air with fixed apex angle $A$, Snell's law gives $r_1=\arcsin (\sin i/n)$, $r_2=A-r_1$ and $e=\arcsin (n\sin r_2)$. The exit angle $e$ is relative to the moving exit-face normal; the deviation $D$ is relative to the incoming beam. Rotating the prism while keeping the incident beam fixed changes the laboratory outgoing direction by $\Delta D$. Steering the incoming beam while fixing the prism instead changes it by $\Delta e$. These are distinct experiments; emergence and total-internal-reflection conditions must also be checked.