Fizeau's Experiment (Speed of light)

In summary, the conversation discusses the Fizeau's Experiment to determine the speed of light using a rotating gear with N teeth, a frequency of f, and a distance of L between the gear and the mirror. The conversation also mentions the use of equations such as speed = distance/time, f = 1/T, and angular frequency(w) = 2πf to solve for the speed of light. Different approaches and solutions are discussed, with the final solution including a term for n eclipses. The significance of n in this experiment is to maintain the series and account for the rotation speed where the light cannot return through a gap.
  • #1
TachyonLord
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6

Homework Statement



In the Fizeau's Experiment to determine the speed of light, let the gear have N teeth, the frequency of the rotating gear being f, the distance traveled by the light beam/ray L (distance b/w the gear and the mirror) and let there be n eclipses(blocking of the light beam).
Calculate the speed of light.
More information on the experiment :
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Homework Equations


$$Speed =\frac {Distance} {Time}$$
$$ f = \frac 1 T$$
Angular frequency(w) = 2πf

The Attempt at a Solution


So I tried solving this by using $$c(speed of light) = \frac {2L} t$$
where T will be the time for the light to pass through the teeth and then be reflected.If T is the time period of the gear, then $$t = \frac T {2N}$$
because I'm thinking that the time for one eclipse should be the time taken to go from A to B, which is equivalent to one tooth's length.
Untitled.png

$$⇒ t = \frac {1} {2fN}$$
And subsequently, c = 4LfN , but this doesn't include n.
So I tried a different approach and used the formula $$t = \frac d v$$
$$d = \frac {2πR} {2N}$$
v = (2πf)R
which again gives the same answer, without the n term.

I also thought of another situation, where the light goes through the gap and is blocked by some tooth(which is not the successive one) which seems absurd in itself and I don't really know how to continue.
The answer that was annouced in the class had something like (2n-1) in the denominator. I don't know where I'm going wrong.
Thank you.
 

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  • #2
TachyonLord said:
because I'm thinking that the time for one eclipse should be the time taken to go from A to B, which is equivalent to one tooth's length.
It is 1/(2N) of one revolution in the first case (n=1), 3/(2N) of one revolution in the second case (n=2) and so on. Can you generalize this?
 
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  • #3
mfb said:
It is 1/(2N) of one revolution in the first case (n=1), 3/(2N) of one revolution in the second case (n=2) and so on. Can you generalize this?
How does it become 3/(2N) for n=2 ? Could you explain ?
 
  • #4
Gap to gap is 1/N, but you have 3/2 of that distance.
 
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  • #5
mfb said:
Gap to gap is 1/N, but you have 3/2 of that distance.
Thank you so much ! After generalising, I'm getting $$\frac {4LNf} {2n-1}$$
Although I'm yet to confirm is this is the answer, but this is what I get. Again, thank you so much !
 
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  • #6
mfb said:
It is 1/(2N) of one revolution in the first case (n=1), 3/(2N) of one revolution in the second case (n=2) and so on. Can you generalize this?
Okay just a teeny doubt, how do you define an eclipse ? I mean I used n in order to maintain the series but like what would be its physical significance ?
 
  • #7
It is a rotation speed where the light can't return through a gap.
 

Related to Fizeau's Experiment (Speed of light)

What is Fizeau's Experiment?

Fizeau's Experiment is an experiment conducted by French physicist Armand Fizeau in 1849 to measure the speed of light.

How does Fizeau's Experiment work?

The experiment involves using a rotating cogwheel with evenly spaced teeth and a stationary mirror placed several kilometers away. A beam of light is shone through the gaps in the cogwheel and reflected back to the source. By measuring the speed at which the cogwheel needs to rotate in order to block the returning light, the speed of light can be calculated.

What was the significance of Fizeau's Experiment?

Fizeau's Experiment was the first successful attempt at directly measuring the speed of light using an optical method. It also provided evidence for the wave theory of light and helped to disprove the competing theory of emission.

What was the result of Fizeau's Experiment?

Fizeau's Experiment yielded a value of 315,000 km/s for the speed of light, which is very close to the currently accepted value of 299,792,458 m/s. This result provided strong support for the wave theory of light and helped to advance the field of optics.

How did Fizeau's Experiment influence future scientific research?

Fizeau's Experiment paved the way for further experiments and advancements in the study of light and optics. It also played a crucial role in the development of Einstein's theory of special relativity, which revolutionized our understanding of the nature of light and its speed.

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