Sagnac Effect (time difference)

The Sagnac Effect Time Difference calculator computes time difference based on the radius of the loop, the angular velocity and the speed of light.

INSTRUCTIONS: Choose units and enter the following

• (R) This is the radius
• (Ω) This is the angular velocity

Time Difference (Δt):  The calculator returns the time difference in seconds.  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Sagnac Effect (time difference) is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer. A beam of light is split and the two beams are made to follow the same path but in opposite directions. To act as a ring the trajectory must enclose an area. On return to the point of entry the two light beams are allowed  to exit the ring and undergo interference. The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted and according to the angular velocity of the apparatus. This arrangement  is also called a Sagnac interferometer.

The formula for the Sagnac Effect time difference is:

         `Deltat=(4piR^2omega)/(c^2-R^2omega^2)`

where: 

• R = radius
• Ω = angular velocity
• c = speed of light

References

Wikipedia (https://en.wikipedia.org/wiki/Sagnac_effect)