Show that the flux density energy is conserved when light is

Show that the flux density (“energy”) is conserved when light is reflected and transmitted at the interface of air (n=1) and glass (n=1.5).

Solution

The speed of light in a medium is inversely proportional to the refractive index, so the
amplitude ratios can be expressed as,
1 : 2n₁ / n₁ + n₂ : n₁- n₂ / n₁ + n₂
We see that there is a phase change on reflection from an optically denser medium.
The flux density ratios can be written as
.1 : 4n₁n₂ / (n₁ + n₂ )² : (n₂ - n₁)² / (n₁ + n₂ )²
If light is going from air (n1 = 1) to glass (n2 = 1.5), the transmitted amplitude will be
80 percent of the incident amplitude, and the reflected amplitude will be 20 percent of the
incident amplitude. The transmitted flux density will be 96 percent of the incident flux
density, and the reflected flux density will be 4 percent of the incident flux density.