It is said that Galileo proposed to measure the speed of light by having two peo

Question

It is said that Galileo proposed to measure the speed of light by having two people with covered lanterns standing far apart. The first person would uncover his lantern. Upon seeing the light from the first lantern, the second person would uncover his lantern. The first person would then note the time it took to see the light from the second lantern. It is also said that Galileo himself tried the experiment with the two people less than a mile apart.

1) Assuming that two people are standing 1 mile (1.6 km) apart, how long would light take to travel from the first person to the second person and back? (s)

2) Given that the the average human reaction time is 0.07 s, how far apart would the two people have to be if the the round-trip travel time for light were to be 0.07 s? (Could this be be done with two people on the Earth's surface?) (s)

3) Around 1676, a half century after Galileo, the Danish astronomer Olaus Roemer found lag times in the predicted eclipses of one of Jupiter's moons, Io, by Jupiter when the Earth was farther away from Jupiter. He concluded these time lags were due to the extra time needed for the sunlight reflecting from Io to cross the extra distance of the Earth's orbit diameter. He concluded that light took an extra 22 minutes to cross the diameter of the Earth's orbit around the Sun. Again, noting that the radius of the Earth's orbit is 1.5 x 108 km, what speed did Roemer calculate for light? (m/s)

4) The error in Roemer's measurement was traced to the time he used for light to cross the diameter of Earth's orbit. How many minutes does it really take for light to cross the diameter of Earth's orbit? (minutes)

Explanation / Answer

Here ,

a) time taken for light to travel = distance/speed of light

time taken for light to travel = 1.6 * 10^3 * 2/(3 *10^8)

time taken for light to travel = 1.067 *10^-5 s

b)

let the distance is d

distance = time * speed of light

distance = 3 *10^8 * 0.07 m

distance = 2.1 *10^7 m

part c)

speed of light = distance/time

speed of light = 2 * 1.5 *10^11/(22 * 60)

speed of light = 2.27 *10^8 m/s

part d)

let the time taken is t

time taken for light to cross = distance/speed of light

time taken for light to cross = 2 * 1.5 *10^11/(3 *10^8)

time taken for light to cross = 1000 s

time taken for light to cross = 16.7 min

the time taken for light to cross is 16.7 min

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