The formula of the length contraction is
Answer to Problem 18P
Formula of the length contraction derived from the experiment as in Figure 2.11 is
Explanation of Solution
Formula used:
Distance travelled by the light from source point to reflection point is as follows:
Distance travelled by the light during return trip is as follows:
Where, L is the length contraction, v is the speed of the moving system, c is the speed of the light,
Formula of the time dilation:
Where
Calculation:
Total time taken by the light to complete a round trip between source point and mirror will be calculated from equation (I) and (II).
Let’s total time is
Now comparing the equation (V) with equation (III)
After simplification
Now substitute the value of
Conclusion:
Therefore, formula of the length contraction derived from the experiment as in Figure 2.11 is
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