Using the diagram shown in figure 20.13, derive the time dilation formula. The steps are:
a. From the symmetry of the diagram, we assume that the total time measured by the Earth observer is twice the time required to reach the mirror.
b. Using the right triangle shown in the diagram and the Pythagorean theorem, we can write 

c. Grouping terms containing t on one side of the equation and taking the square root of both sides, we can solve this expression for the time t measured by the Earth observer.
d. Since the quantity 2d/c is the time measured by the spaceship pilot t₀, this expression reduces to the time dilation formula introduced in section 20.3.

2 2 2 2 (3)-