180 degree phase shift of reflected light

[ramsd]

When light originating from a medium of lower refractive index reflects off a surface of higher refractive index, why does the phase shift by 180 degrees? Stokes relations show that reflection coefficients at the surface are equal but of opposite signs depending on direction of light (i.e. from lower to higher refractive index versus higher to lower); but Stokes relation does not tell me explicitly which one is shifted by 180 degrees. Can someone please provide an explanation for this. I have researched the internet with no success. Thank you in advance.

 

[Baluncore]

The magnetic component of the incident ray induces a perpendicular current in the mirror. That current generates a perpendicular magnetic field, that cancels the incident ray into the mirror.
The energy that is reflected is due to the current flowing on the mirror surface.

i·i = i² = -1.
Rotating 90° twice makes 180°.

 

[ramsd]

The magnetic component of the incident ray induces a perpendicular current in the mirror. That current generates a perpendicular magnetic field, that cancels the incident ray into the mirror.
The energy that is reflected is due to the current flowing on the mirror surface.

i·i = i² = -1.
Rotating 90° twice makes 180°.

Thanks Baluncore, that clears it up.