10. Provide the time dilation equation found in Section 15.4 of the text. Explain each step of the derivation.

T=t_0 / (√ (1 - (V/C)) ^2) Equation

The symbol to represents the time it takes for the flash to move between the mirrors as measured from a frame of reference fixed to the light clock. Since the speed of light is always c, the light flash is observed to move a vertical distance cto in the frame of reference of the light clock. This is the distance between mirrors. This vertical dis - tance is the same in both reference frames. The symbol t represents the time it takes the flash to move from one mirror to the other as measured from a frame of reference in which the light clock moves to the right with speed v. Since the speed of the flash is c and the time to go from position 1 to posi - tion 2 is t, the diagonal distance traveled is ct. During this time t, the clock moves a horizontal distance vt from position 1 to position 2.