Discussion
The shadowgraph flow visualization technique depends on
Answer: C
The shadowgraph depends on the second derivative of density with respect to spatial coordinate.
Light is bent by refractive index gradients, and refractive index varies linearly with density. In a shadowgraph the light rays are deflected and then allowed to spread before reaching the screen, so the change in illumination depends on how the deflection varies across the field, which is the second derivative \(\partial^{2}\rho/\partial x^{2}\).
The schlieren method responds to the first derivative of density, and interferometry measures density itself. No common optical method responds to the third derivative.
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