(a) A light pulse emitted at the rear of the spaceship (event E,) arrives at the front (event E,). In the spaceship frame, S', the time interval between E, and E, is '-t = L/c. Find the time interval between the same two events in frame S, in terms of L, V, and c. (See fig. 2.3a. Note that this time interval is not proper in either frame.) (b) The light pulse is reflected and arrives at the rear of the spaceship (event E3). Find the time interval between E, and E, in frame S. (c) Applying a proper time argument to the interval between E, and Eg, show that L and Lg are related by the length contraction formula: L= L Vĩ - VIe.

 For this problem, pretend that you do not know about length contraction but
you do know about time dilation.
A spaceship whose length in its own rest frame is La moves at velocity V
relative to earth. Let L be the length of the spaceship as measured in the earth's
rest frame, S.

(a) A light pulse emitted at the rear of the spaceship (event E1) arrives at the
front (event E2 ). In the spaceship frame, Sf, the time interval between E1 and E2 is
t f - t~ = L
o/ c. Find the time interval between the same two events in frame 5, in
terms of L, V, and c. (See fig. 2.3a. Note that this time interval is not proper in
either fralne.)
(b) The light pulse is reflected and arrives at the rear of the spaceship (event
£3)' Find the time interval between £2 and E3 in frame S.
(c) Applying a proper time argument to the interval between E1 and E3 , show
that Land Lo are related by the length contraction formula: L = Lo~1- V 2/ c2 .