Maxwell's Rainbow — Question 5

Question 5

Measured arrival differences can reflect emission timing instead of vacuum dispersion

A distant source emits an optical pulse and a radio pulse along the same vacuum path. The radio detector has an additional calibrated electronic delay of 8 microseconds. The recorded radio arrival is 23 microseconds after the optical arrival. Both waves propagate at c.

1. Infer the radio emission delay relative to the optical emission.

2. If the common source distance doubles while emission timing and detector delays stay fixed, find the new recorded delay and explain the cancellation.

Question 5 - Solution

Measured arrival differences can reflect emission timing instead of vacuum dispersion

(a) Method and calculation

$$t_{r,\mathrm{rec}}=t_{r,\mathrm{emit}}+L/c+8\,\mu\mathrm s,\quad t_{o,\mathrm{rec}}=t_{o,\mathrm{emit}}+L/c.$$$$\boxed{t_{r,\mathrm{emit}}-t_{o,\mathrm{emit}}=23-8=15\,\mu\mathrm s}.$$

(b) Interpretation and further calculation

$$\Delta t_{\mathrm{rec}}(2L)=\Delta t_{\mathrm{emit}}+2L/c-2L/c+8\,\mu\mathrm s.$$$$\boxed{\Delta t_{\mathrm{rec}}(2L)=23\,\mu\mathrm s}.$$

Physical check

Arrival-time comparisons require emission and instrument timing; a nonzero measured delay alone does not establish different vacuum speeds.