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Light's internal reflectivity near a critical angle is very sensitive to theangle of incidence and the optical properties of the external medium near theinterface. Novel applications in biology and medicine of subcritical internalreflection are being pursued. In many practical situations the refractive indexof the external medium may vary with respect to its bulk value due to differentphysical phenomena at surfaces. Thus, there is a pressing need to understandthe effects of a refractive-index gradient at a surface for near-critical-anglereflection. In this work we investigate theoretically the reflectivity near thecritical angle at an interface with glass assuming the external medium has acontinuous depth-dependent refractive index. We present graphs of the internalreflectivity as a function of the angle of incidence, which exhibit the effectsof a refractive-index gradient at the interface. We analyse the behaviour ofthe reflectivity curves before total internal reflection is achieved. Ourresults provide insight into how one can recognise the existence of arefractive-index gradient at the interface and shed light on the viability ofcharacterising it.

Detecting and analysing wavelength-scale optical gradients at an interface by their effects on the internal reflectance near the critical angle