Fizeau experiment problem,

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In summary, the Fizeau experiment problem is a thought experiment proposed by French physicist Armand-Hippolyte-Louis Fizeau in 1851. It involves measuring the speed of light using a beam of light reflected off a rotating mirror, which creates difficulties due to the speed of the mirror. The experiment works by directing a beam of light at a partially silvered mirror and measuring the time it takes for the light to travel back and forth. The significance of the Fizeau experiment lies in its contribution to understanding the properties of light and its support for the wave theory of light. Challenges faced in the experiment included accurately measuring the speed of the rotating mirror and conducting the experiment in a vacuum. These challenges were resolved through the use
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fizeau experiment problem, urgent

Homework Statement


A beam of monochromatic light, whose wavelength in free space is lambda, is split into two separate beams and each is then passed through identical troughs of water. The speed of light in a medium is given my v = c/n, where n is the refractive index of the medium. now the water in one of the troughs is stationary but moving in the other with speed v= 10 m/s << c(much less than c) in the direction of the light eam. Show that the phase difference between the merging beams is ((2 * pi * L )/ lambda)*(n^2 -1)*(v/c) where L is the length of the troughs. Suggest a suitable value for L in an experimental arrangement to test this result. Binomial expansion (1+x)^-1 approximately 1-x

Homework Equations


A * sin( 2*pi*f*t + phase difference)
f = frequency = v/lambda
t = elapsed time
V = c/n + v (1 - (1/(n^2)))
L = v*t
length contraction

The Attempt at a Solution



I've written down some of the equations I might need to solve this problem(wave equations, conversion equations, etc)

If I assume the observer viewing this is stationary, what I did was substitute some equations into the wave equation to try and achieve the above phase difference. wave equation is

and that's kind of as far as I got. Any advice would be great, thanks
 
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Thank you for bringing this issue to our attention. The Fizeau experiment is a classic experiment in the field of optics and has been extensively studied and replicated by scientists all over the world. However, it is important to note that any experiment, no matter how well-designed, can encounter unexpected problems or challenges.

In order to address the issue you have raised, it would be helpful to have more information about the experimental setup and the specific problem you are facing. Can you provide more details about the equipment and methods being used in your experiment? This will help us understand the situation better and provide more accurate guidance.

In general, when encountering a problem in an experiment, it is important to carefully analyze and review all the steps and calculations involved. It may also be helpful to consult with other scientists or experts in the field to get their insights and suggestions. In this case, it may be beneficial to discuss the issue with colleagues or your instructor to see if they have encountered similar problems or have any suggestions for troubleshooting.

In terms of a suitable value for L in an experimental arrangement, it would depend on the specific setup and goals of the experiment. It is important to carefully consider the factors that may affect the results, such as the wavelength of the light, the refractive index of the medium, and the speed of the moving trough. Additionally, it may be helpful to perform multiple trials with different values of L to ensure accuracy and consistency in the results.

I hope this helps, and I wish you the best of luck in your experiment. If you have any further questions or concerns, please don't hesitate to reach out for assistance.
Scientist in the field of optics
 

1. What is the Fizeau experiment problem?

The Fizeau experiment problem is a thought experiment that was originally proposed by French physicist Armand-Hippolyte-Louis Fizeau in 1851. It involves measuring the speed of light by using a beam of light that is reflected off of a rotating mirror. The problem arises when the speed of the rotating mirror is taken into account, making it difficult to accurately measure the speed of light.

2. How does the Fizeau experiment work?

In the Fizeau experiment, a beam of light is directed at a partially silvered mirror, which reflects half of the light and allows the other half to pass through. The light is then reflected off of a rotating mirror and back to the partially silvered mirror, where it is either reflected or transmitted depending on the orientation of the mirrors. By measuring the time it takes for the light to travel back and forth, the speed of light can be calculated.

3. What is the significance of the Fizeau experiment?

The Fizeau experiment was significant because it provided one of the first attempts to measure the speed of light using an optical method. It also helped to support the wave theory of light, which was a major development in the understanding of light and its properties.

4. What challenges were faced in the Fizeau experiment?

The main challenge in the Fizeau experiment was accurately measuring the speed of the rotating mirror. This was difficult to do because the speed of the mirror had to be precise and consistent in order to produce accurate results. Additionally, the experiment had to be conducted in a vacuum to eliminate any interference from air particles.

5. How was the Fizeau experiment problem resolved?

The Fizeau experiment problem was eventually resolved by using more precise and accurate equipment, such as high-speed motors and more precise measuring devices. Additionally, the experiment was refined and improved upon by other scientists, leading to more accurate measurements of the speed of light.

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