A laboratory has constructed a straight, evacuated tube of length L whose interior pressure can be switched between near-vacuum and normal atmospheric conditions without otherwise altering the apparatus. A pulsed laser installed at one end sends light through the tube to a photodetector at the other end.
When the tube is filled with dry air (index of refraction n) the detector records the arrival time of the pulse as tair. When the tube is evacuated, the arrival time is t0. Air behaves nondispersively for the laser’s wavelength.
Scientists want to derive a general expression for the travel-time difference Δt=tair−t0 and then evaluate it numerically.
(a) Derive, in symbolic form, an expression for Δt in terms of L, n, and c.
(b) Using L=500m and n=1.00029, calculate Δt.
(c) Explain how this experiment empirically demonstrates whether electromagnetic waves require a material medium for their propagation.
(d) Comment on how increasing the tube length by an order of magnitude would affect both Δt and the experimental evidence regarding the need for a medium.