Reproducing Lance Osadchey's Velador Experiment

(Last Reviewed 6/5/07) 

Refraction by thermal gradients within the air inside the beam must be considered.  Any radial thermal gradient can potentially refract the laser beam. 

Snell’s law for refraction of a one dimensional light ray at a 2 dimensional plane interface (such as an air/water interface) is given in equation 8.

The variables are:

n₁ and n₂ are the indexes of refraction on sides 1 and 2 of the plane interface

θ₁ is the angle of incidence on side 1 of the interface, measured from the normal vector

θ₂ is the angle of transmission on side 2 of the interface, measured from the normal vector

Note that as θ₁ approaches 90 degrees (where the incident beam is nearly parallel to the interface plane), θ₂ does not change as rapidly as the angle of incidence.  This creates a relatively sharp turn in the angle of the transmitted light, which can approach 90 degrees for the theoretical worst case.  In this instance, no incident light would reach the camera sensor, or even the other side of the support beam.  However, the laser beam is not one dimensional, nor is the interface two dimensional.  Thus, this approximation breaks down at the interface.  Portions of the incident laser beam will experience refraction through a greater angle than others, spreading the laser beam.  A strictly radial thermal gradient will most likely manifest itself through spreading of the laser beam.  Laser beam path deflection can also occur in the presence of a significant axial gradient combined with a radial gradient.  Although beam spreading will not be as prominent for an additional axial gradient, it should still occur at some reduced level.  Thus, the total area of the incident light should be monitored to check for changes due to possible thermal effects.