When a light (or any other EMW) is striking a reflecting surface it is expected that it would reflect back with same angle as of incidence with normal to the point. Considering wave nature of light, light is a resultant of electric field and magnetic field. So at point when light is reflecting what could be expected about Electric and Magnetic fields? Do the reflect as sharp point? If they reflect as sharp point wouldn't there be non differentiable point leading to either many or non directions for light and fields!

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If you want to examine the reflection of light in detail as it happens, physically, at the interface, then the geometrical-optics model of light as a ray that propagates in straight lines will simply not be sufficient. Instead, you need to think about wave optics, i.e., visualising light as a wave, and looking at its behaviour at lengthscales close to the wavelength.

For the case of (total) reflection, the intensity of light never drops discontinuously between one medium and the other (or indeed anywhere else at all!). Instead, if a light comes in on medium 1, impinges on a planar interface with medium 2, and completely reflects off of the interface, then within medium 2 you will get a small remnant of the wave. This is called an evanescent wave, and it vanishes quickly (exponentially) as you get into the medium and away from the interface.

For light, this exponential decay is typically too fast to detect explicitly. However, for microwaves (which are the same thing as light, just with a much more manageable lengthscale) the corresponding experiment, known as microwave tunnelling and explained e.g. here, is a long-time classic demonstration.

If you want a good understanding of what the light "actually" looks like as it transitions from "normal wave" to the exponentially-decaying evanescent field, this previous answer of mine has good animations of the time evolution of the spatial dependence of the field which are a bit more complete (in that they include the reflected wave) than the equivalent on Wikipedia.


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