Contd...

Let be the final; illumination on the screen after the light beam has deflected upwards by an amount due to the inhomogeneous distribution of refractive index gradients in the test cell. Hence

(6)

The change in the light intensity on the screen is given by

The relative intensity or contrast can be expressed as

(7)

Using Equation 5

(8)

Equation 8 shows that the contrast in a schlieren system is directly proportional to the focal length of the second lens. Larger the focal length, greater will be the sensitivity of the system.

Combining Equations 3 and 8

(9)

This equation shows that the schlieren technique records the average gradient of refractive index over the path of the light beam. If the field is two dimensional with the refractive index gradient constant at a given position over the length in the direction, then

(10)