If the refrective index within the test section is different from that of the ambient air , then from Snell's law, the angle of the light beam after it has passed through the test section and emerged into the surrounding air is given by

For small values of ,

Therefore, Equation 2 gives

If the factor within the integrand does not change greatly through the test section, then

Let be the length of the test section along the direction of the propogation of the light beam. Since the cumulative angle of refraction of the light beam emerging into the surrounding air is given by

(3)

A schlieren system is basically a device to measure the angle , typically of the order of rad, as a function of position in the x-y plane normal to the light beam. Consider the system shown in Figure 5.3. A light source with dimensions is kept at the focus of lens and provides a parrallel beam of light which probes the test section.

Figure 5.3: Schematic showing the path of light beam in a typical schlieren system

The dotted lines shows the path of the light beam in the presence of disturbances in the test region. The second lens , kept at the focus of the knife-edge collects the light beam and passes onto the screen located at the conjugate focus of the test section.