In this problem, we consider a light clock a clock that ticks every time light m

Question

In this problem, we consider a light clock a clock that ticks every time light makes a round trip between two mirrors separated by a distance L The key point is that we can deduce the rate at which this clock ticks, when it moves relative to us as well as when it is at rest, directly from the postulates of special relativity. The postulates of special relativity are as follows: 1. The laws of physics are the same in any coordinate system that moves at constant velocity (i.e., any inertial reference frame). 2. The speed of light is c when measured with respect to any coordinate system moving at a constant velocity. As shown in the figure, the light clock is based on the propagation time of light Light between mirrors spaced a Clock distance L a in the rest frame of the clock. As the light bounces back and Pulses each forth between the mirrors, a small bit of light is allowed to escape through the partially silvered lower mirror. These transmitted pulses of light hit a detector, which therefore emits evenly spaced (in time) 'ticks" each round-trip time of the pulse. (New pulses are injected in phase with the detected pulses to keep the clock going.) In this problem, we show that if the clock is moving with speed v relative to a reference frame S, then the ticks from the clock appear slowed when viewed from S. The key is to calculate explicitly the path length of the light pulses as seen in the frame S. From that you can find the length of time that an observer in Swill measure between Ticks of the relatively moving clock. We consider the case where the clock is moving perpendicular to its long axis as shown. Considering a "thought experiment (Gedankenexperiment in German)like this allows us to calculate the tick rate of the clock when viewed by the observer in S. Einstein used Gedanken experiments like this to clarify his thinking as he strove to remove inconsistencies in the basic formulations of physics.

Explanation / Answer

from the right angle triangle formed by the light path with the direction of motion of the clock:

base of the triangle=length covered by the clock

=speed of the clock*time

=v*ts/2

height=L

then Ls=sqrt(height^2+base^2)

=sqrt(L^2+(v*ts/2)^2)

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