Contd...

The scale factor used in calculations is derived below.

Applying Snell's law for refraction of the light ray passing from the KDP-solution into the quartz optical window, we get

(46)

where are the angles of incidences of the light at the quartz window, the angle of refraction of the light ray into the quartz window, the refractive index of the KDP solution, and the refractive index of the quartz window respectively. Applying Snell's law again for the ray passing from the quartz optical window to the surrounding air, we get

(47)

where are the angles of refraction of the light ray into the quartz window, the angle of refection of the light ray in the air, the refractive index of the quartz window, and the refractive index of air respectively. Substituting the expression for from Equation 46 into Equation 47, we get

Under the small-angle approximation sin , and

Hence

(48)

Thus the correction factor for additional refraction at the optical windows is .