The objective of this experiment is to measure the speed of light in an optical fiber by measuring the time a light signal takes to traverse a known length of fiber.
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If a light signal travels a length ΔL in a medium of refractive index, n in time Δt, then the constant speed of light in that medium can be determined simply as cn = ΔL/Δt. The refractive index of a medium is n = c/cn, where c is the speed of light in vacuum.
The basis of this experiment is very simple. An LED (light emitting diode) is energized by a square voltage pulse. The time, Δt of travel of the resulting light pulse emitted by the LED, through the fiber of length ΔL, is measured and used to compute the speed of light. But here is the caveat. Since Δt is only tens of nanoseconds, and the signals from Channel 1(CH-01) and Channel 2(CH-02) travel through different electrical paths considerable errors can be introduced in the measurement of Δt. Therefore, the actual experimental execution of the measurement scheme outlined above is a bit more interesting. Suppose you tap the square pulse signal (divert part of it) at the input end of the LED and use its detection as t = 0.0sec. It is instructive to know the various time delays that can be introduced before the signals of CH-01 and CH-02 are detected and displayed on the oscilloscope.
We have to make sure that the time delay we are measuring is only the time delay caused by the light traveling from O to I through the fiber and not due to any other electrical delays. The time delay between CH-01 and CH-02 can be expressed as ΔT =Δt +Δt’ where Δt is the time light takes to travel through the fiber and Δt’ is the total differential time delay between CH-01 and CH-02 due to different electrical paths the signals travel through the two channels. In most experiments such differential time delays are of little concern and are often neglected. However, in the present experiment Δt ~100 ns and Δt’ has to be properly compensated for. To do this we have to calibrate the time axis, as detailed below, by finding ΔT when Δt ~ 0. This is done by using a short length (15cm) of an optical fiber and measuring ΔT. For a 15 cm fiber Δt ~ 0.75 ns and thus ΔT0 =Δt +Δt’ = 0.75ns +Δt’. Since the expected Δt ~ 100ns for a 20m fiber, ΔT0 = 0.75ns +Δt’ can be taken as a reasonably accurate measure of the differential electrical delay between CH-01 and CH-02. Thus if we subtract ΔT0 from our time delay measurements, we can extract the time the light signal takes to travel through a given length of optical fiber.
The SOL Apparatus is now CALIBRATED!
What is the value of the speed of light in vacuum?
How does the speed of light depend on the refractive index of the medium of propagation of light?
From your text find the values of the refractive indices of
[a] Air
[b] Water
[c] Glass