Module 5: Schlieren and Shadowgraph
  Lecture 26: Introduction to schlieren and shadowgraph
 

Assumption 1. Assume that the light rays incident normally at the entrance plane undergo only infinitesimal deviations inside the inhomogeneous field, but have a finite curvature on exiting the chamber. The derivatives at the exit plane have finite values. The assumption is justifiable because of the smoothly varying refractive index in a fluid medium. Under this assumption Equations25 and 28 become

(30)
(31)
(32)
(33)

Rewriting the Equations 32 and 33 as

(34)
(35)

and using Equations 30 and 31, Equations 34 and 35 become

(36)
(37)