Question

You and your friend carry identical clocks. Your friend passes by in a rapidly moving train. As your clock ticks off 1.00s, you see your friend’s clock tick off 0.50s. How much time would your friend see your clock tick off in the time it takes your friends clock to tick off 1.00s?

Answer 1

Time period of friend's clock,

Time observed in the stationary observer's frame

According to theory of relativity:

Here v is the velocity of the train in which friend is travelling

In the friends frame, he/she is stationary but the otherwise stationary observer i.e. myself will appear to him/her move with relative velocity 'v'

Let that friend observes the time period to be of the stationary observers clock when actual time in his frame is 1.00 s

Therefore

Comparing (1) and (2)

Therefore friend will see my clock tick off 0.50 s during the time his/her clock tick off 1.00 s