handbook of modern sensors

4.1 Radiometry 127
Fig. 4.4. Light passing through an optical plate.
Before light exits the second medium (Fig. 4.2) and enters the third medium having
refractive index n 3 , another part of it is reflected internally from the second boundary
between the n 2 and n 3 media at angle ′ 2
. The remaining portion of light exits at angle
3 , which is also governed by Snell’s law. If media 1 and 3 are the same (e.g., air) at
both sides of the plate, then n 1 = n 3 and 1 = 3 . This case is illustrated in Fig. 4.4.
It follows from Eq. 4.5 that the coefficients of reflection are the same for light striking
a boundary from either direction—approaching from the higher or lower index of
refraction.
A combined coefficient of two reflections from both surfaces of a plate can be
found from a simplified formula:
ρ 2 ≈ ρ 1 (2 − ρ 1 ), (4.7)
where ρ 1 is the reflective coefficient from one surface. In reality, the light reflected
from the second boundary is reflected again from the first boundary back to the second
boundary, and so on. Thus, assuming that there is no absorption in the material, the
total reflective loss within the plate can be calculated through the refractive index of
the material:
ρ 2 = 1 −
2n
n 2 + 1 . (4.8)
The reflection increases for higher differences in refractive indices. For instance, if
visible light travels without absorption from air through a heavy flint glass plate,
two reflectances result in a loss of about 11%, whereas for the air–germanium–air
interfaces (in the far-infrared spectral range), the reflective loss is about 59%. To