  We analyze the transparency of a thin film of low refractive index (an
optical glue or a bonding layer) placed between higher-index media and forming
an opto-pair. Examples include a semiconductor light-emitting diode with
attached lens or a semiconductor scintillator bonded to a photodiode. The
transparency of an opto-pair is highly sensitive to the film thickness due to
the so-called frustrated total internal reflection. We show that high
transparency in a wide range of the incidence angle can be achieved only with
very thin layers, more than an order of magnitude thinner than the wavelength.
The angular dependence of the transmission coefficient is shown to satisfy a
simple and universal sum rule. Special attention is paid to the angular average
of the optical power transmission, which can be cast in a universal form for
two practically relevant classes of source layers.
