The Postulates — Question 3

Question 3

A departing mirror fixes a common reflection event

A mirror follows $x=L+vt$, while a source remains at $x=0$. A pulse leaves at $t=0$, reflects once, and returns to the source. Let $L=600\,\mathrm m$, $v=0.20c$, $c=3.00\times10^8\,\mathrm{m/s}$. Ignore mirror recoil.

1. Find the reflection time and position in the source frame.

2. Find the return time and compare the two legs in that same frame.

Question 3 - Solution

A departing mirror fixes a common reflection event

(a) Method and calculation

$$ct_1=L+vt_1\quad\Rightarrow\quad t_1=\frac{L}{c-v}=2.50\,\mu\mathrm s.$$$$\boxed{x_1=ct_1=750\,\mathrm m}.$$

(b) Interpretation and further calculation

$$t_2-t_1=\frac{x_1}{c}=t_1,\qquad\boxed{t_2=5.00\,\mu\mathrm s}.$$$$\boxed{t_{\mathrm{out}}=t_{\mathrm{back}}=2.50\,\mu\mathrm s}.$$

Physical check

The reflected path ends at the fixed source. The mirror moves, but both legs span the same laboratory distance to the reflection event.