Physics
Speed of Light
Fizeau Method
11
⚡ Quick Summary
The Fizeau method uses a rotating toothed wheel to chop a light beam into pulses. By measuring the speed at which the wheel needs to rotate to block the returning light after it travels a known distance to a mirror and back, the speed of light can be calculated.
['θ = 2π / (2n) (angle rotated by the wheel when a tooth comes in the place of its adjacent gap)', 'c = 2D / (π / (nω)) = 2Dnω / π (speed of light)', 'c = 4Dnν (speed of light, where ν is the number of revolutions per unit time and ω = 2πν)']
- A beam of light is directed towards a toothed wheel.
- The light passes through a gap between the teeth.
- A lens makes the light parallel, and it travels a long distance to a mirror.
- The mirror reflects the light back towards the wheel.
- If a tooth is in the way when the light returns, the light is blocked.
- By increasing the wheel's rotation speed, a point is reached where the returning light is consistently blocked by a tooth.
- Measuring the wheel's speed and knowing the distance the light traveled allows for calculating the speed of light.
Foucault Method
11
⚡ Quick Summary
The Foucault method uses a rotating mirror to reflect a beam of light. The angle of the reflected beam changes as the mirror rotates. By measuring the shift in the image position due to the mirror's rotation, the speed of light can be calculated.
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- Light from a source is partly transmitted by a glass plate.
- The light is incident on a convex lens, making the beam convergent.
- A rotating plane mirror reflects the light onto a concave mirror.
- The concave mirror reflects the light back to the rotating plane mirror.
- Due to the rotation of the plane mirror, the returning light is slightly deviated.
- This deviation results in a shift in the image position.
- By measuring the shift and knowing the parameters of the setup, the speed of light can be determined.
Michelson Method
XI
⚡ Quick Summary
Michelson's method involves using a system of mirrors, including a rotating polygonal mirror, to measure the speed of light by accurately timing how long it takes for light to travel a known distance. By adjusting the rotational speed of the polygonal mirror until the reflected light is visible in a telescope, the speed of light can be calculated.
['Δt = D/c (Time taken by light to travel distance D)', 'Δθ = 2π/N (Angle rotated by the mirror)', 'ω = Δθ/Δt = (2π/N) / (D/c) = 2πc / DN', 'c = DωN / 2π', 'c = DνN (where ν = ω/2π is the frequency of rotation)']
The Michelson method utilizes a polygonal mirror to measure the speed of light. Light from a source (S) is directed onto one face of the polygonal mirror (M). The reflected light travels through a series of mirrors (M1, M2, M3, M4, M5) over a long distance (D) before returning to the polygonal mirror. The rotational speed of the polygonal mirror is adjusted such that when the light returns, the adjacent face of the mirror is in the correct position to reflect the light into a telescope. By measuring the angular speed (ω) of the mirror when the image is steady, the speed of light (c) can be calculated.