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Most spectacles and camera lenses today are coated to reduce reflection. The coating produces another reflection on its own surface, which interferes with the original reflection from the glass surface, reducing the reflection as a result.
Recalling high-school or college science, the coating should be quite precisely made to a thickness of 1/4 of the wavelength of light (in the coating material). The coating thickness is of the order of 100 nm (nanometre).
When an ordinary cloth is used to rub grease off the glass, the grease becomes an additional coating with varying thickness. This produces multi-coloured reflections, because light is made up of different colours (i.e. different wavelengths). The 'rainbow' effect is similar to what we see when looking at a wet road with an oil film on it.
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