The Postulates — Question 6

Question 6

A light pulse in glass does not test vacuum-speed invariance directly

A slab is at rest in a laboratory and has nondispersive refractive index $n=1.50$. Its thickness is $d=0.90\,\mathrm m$. Compare a pulse crossing the slab with a vacuum pulse crossing the same distance. Use $c=3.00\times10^8\,\mathrm{m/s}$.

1. Find both transit times and the slab delay.

2. Identify the physical rest frame introduced by the material and explain why the measured speed $c/n$ does not contradict the vacuum postulate.

Question 6 - Solution

A light pulse in glass does not test vacuum-speed invariance directly

(a) Method and calculation

$$u_{\mathrm{slab}}=c/n,\qquad t_{\mathrm{slab}}=nd/c=4.50\,\mathrm{ns}.$$$$t_{\mathrm{vac}}=d/c=3.00\,\mathrm{ns},\quad\boxed{\Delta t=1.50\,\mathrm{ns}}.$$

(b) Interpretation and further calculation

$$\boxed{u_{\mathrm{slab}}=2.00\times10^8\,\mathrm{m/s}<c}.$$$$\text{Material rest frame:}\quad v_{\mathrm{slab}}=0;\qquad\text{vacuum: }|u|=c.$$

Physical check

Matter provides a measurable local rest frame for the medium; the relativity principle does not assert that every environment looks identical.