A Sagnac Inteferometer is a rotation detector, but it is incapable of detecting its linear movement in space.
This webapp is setup using two methods of calculating the effect of motion on the fringe shift seen in a Sagnac interferometer. Equation 1 method is the most common
method, using the angular velocity and area of the loop to determine the fringe shift. Supplied herein is a second method (Equation 2) which uses addition of velocities (based
on the equations of Lorentz) to calculate the fringe shifts expected. Conditions similar to the Michelson-Gale experiment are pre-loaded to demonstrate that the fringe shifts
expected for the Earth's rotation alone (z-axis = vertical) using Eq.1 and Eq.2 match to a good approximation. The use of the Equation 2 method allows for the convenient
addition of the Lorentz contraction factor to see how a real Lorentz contraction of the path would affect the fringe shift. The Lorentz contraction fringe shift is the only visible effect
related to the translational velocity. Eq.2 allows for the expression of the time difference in terms of velocities of light differences around the paths as seen by an observer at rest
with the interferometer. The red and blue columns are for calculating the time of light propagation for each arm. The Eq.2 method also allows for the effect of the translational velocity
of the interferometer, and show that this velocity is undetectable (cancels around the arms) as with other interferometers. The latitude parameters are for inputting your latitude on the
Earth's surface. Once this is done, the Earth rotation values will be calculated automatically for three different axis alignments of the interferometer (Vertical, NS and EW). All the
other user input parameters control the Regular Rotation/Translation values calculated using the Equation 2 method. This includes loop length (circumference of the light path), frame
velocity (how fast the device is moving in a straight line), rotational velocity (how fast the device is rotating around its axis), the refractive index of the light path (for example, fibre optic
cable is RI= 1.467), the wavelength of the light in meters, and whether or not to assume a real Lorentz contraction of the path (YES/NO, calculated in a separate box). Click on the
calculate button after inputting the test values. Various input values can be tried to see how it effects the propagation time difference for two counter-propagating beams of light in the
loop, and how much of a fringe shift this results in when the interference pattern is viewed at the detector.