R2B.9 Suppose you are in an inertial frame in empty space with a clock, a telesc
ID: 1770970 • Letter: R
Question
R2B.9 Suppose you are in an inertial frame in empty space with a clock, a telescope, and a powerful strobe light. A friend is sitting in the same frame at a very large (unknown) distance from your clock. At precisely 12:00:00 noon according to your clock, you set off the strobe lamp. Precisely 30.0 s later, you see in your telescope the face of your friend's clock illuminated by your strobe flash (a) How far away is your friend from you (in seconds)? (b) What should you see on the face of your friend's clock if that clock is synchronized with yours? Describe your reasoning in a few short sentencesExplanation / Answer
Let us assume that the friend at some distance 'd'. The strobe of light I sent took 30 seconds to reflect back from friend's clock and reach back to me. Hence,light first travelled 'd' distance from you to friend, and then again 'd' distance while coming back to you. So light travelled total distance of '2d' in 30 seconds. Hence it would take 15 seconds to travel 'd' distance. That means my friend is 15 seconds far away from me.Now speed of light is roughly 3 x 108 m/s . So total distance travelled by light in 15 seconds is
d = speed of light x time taken
= 3 x 108 x 15
d = 4.5 x 109 metres (distance between me and my friend)
(b) As the light is taking 15 seconds to reach from my friend's clock to me, so, the information I'll recieve from him will be 15 seconds late. That means, I will see that his clock is 15 seconds back than my clock time. So when I'll recieve the light, my clock will be showing 12:00:30 pm while his clock will be showing 12:00:15 pm .
This is why, for example when we look up at a galaxy 3 light years away, meaning that it took light 3 years to reach us from that galaxy, we are actually looking at how galaxy looked 3 years before.
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