The phenomenon, which is not due to total internal reflection is

Total internal reflection occurs when light attempts to pass from a denser to a rarer medium at an angle exceeding the critical angle, $i_c = \arcsin\left(\frac{n_2}{n_1}\right)$ for $n_1 > n_2$.

Mirage formation involves refraction and TIR; light from the sky reflects off hot, rarer air layers near the ground.

Diamond brilliance results from multiple TIRs within the gem due to its high refractive index and low critical angle.

Apparent depth arises solely from refraction at the water-air interface, governed by $n_{\text{water}} \sin \theta_{\text{water}} = n_{\text{air}} \sin \theta_{\text{air}}$, with no TIR involved.

Optical fibers rely on TIR; light reflects along the core-cladding interface when incidence exceeds $i_c$.

The phenomenon not due to total internal reflection is the difference between apparent and real depth of a pond.

The final answer is $\boxed{C}$.