Determine an expression for the total travel time of the light pulse, as measured by the following:
A) an observer in the S frame (Use the following as necessary: c, d, and v.)
B) an observer on the spacecraft (Use the following as necessary: c, d, and v.)
What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following
C) an observer in the S frame (Use the following as necessary: c, v, and λT.)
D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)
a) when light pulse moves towards the mirror from spacecraft,distance traveled by the light pulse is d.
When light pulse reflected back towards the spacecraft, distance traveled by light pulse is given by,
d'=d-vt
So the total distance traveled by light pulse is given by,
D=d+d'
D=d+(d-vt)
D=2d-vt.....(1)
Where v is a speed of the spacecraft.
The speed of light pulse is given by,
ct=2d-vt
ct+vt=2d
t(c+v)=2d
Thus the total travel time of the light pulse when observer in the S frame is
b)
Since the length contraction, the distance between spacecraft and mirror is given by
When light pulse reflected back towards the spacecraft, distance traveled by light pulse is given by,
d'' =d' -vt
So the total distance traveled by light pulse is given by,
D=d'+d''
D=d' +(d' -vt)
D=2d'-vt
The speed of light pulse is given by,
Thus the total travel time of the light pulse when observer on the spacecraft is
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