Corrections to jwbensley <at> gmail <dot> com

Loss Notes:
Rough Fibre Loss Budget:
~ 0.25dB loss per 1Km at 1550nm, ~0.35dB at 1310nm.
<= 0.1dB loss per splice.
<= 0.5dB loss per back to back APC connector.

Copper Loss for xDSL (a range of frequencies are typically used and the loss is different across the frequencies!):
In the UK BT specify on a 0.5mm copper line roughly 1.18dB loss at 800Hz, 1.79dB at 1600Hz. No PSTN line is ever a single continous strand of copper though.

Latency Notes:
An often-quoted rule of thumb for fibre latency is 0.5µsec per Km, ~200Km per 1msec.
A raw calculation of c(meters/s)*0.6/1000 == (299792458*0.6)/1000/1000 == 179.87Km per 1msec / 0.89Km per 0.5µsec.
Using a slightly more realistic number for the speed of light in a single mode fibre produces: (299792458*0.68)/1000/1000 == 203.85Km per 1msec / 1.01Km per 0.5µsec.

Default c value (meters per second): 299792458
(Or if you prefer 299792.458 kilometers, or if you'r a dick, 299.792458 megameters).
Refractive index of light in air is 1.
Typical SMF radius 4.5µm, typical MMF is 32.75µm or 26µm.
Typical wavelength for SMF in µm's is 1.31µm or 1.55µm and for MMF 0.85µm.
MMF has a much higher Numerical Aperture which helps to maintain total internal reflection for all modes of light entering the fibre.

Fibre Properties

Refractive Index (N1 is always > N2)
N1 (Core Index)
N2 (Cladding Index)
NA = √(N12)-(N22)
Critical Angle
Acceptance Angle

V Number
λ [µm] (Wavelength)
a [µm] (Core Radius)
V = (2πa/λ)NA
Single Mode <= 2.405
Number of modes:

Speed of Light

Speed of Light in Core (meters/s)
c (meters/s)
N1 (Core Refractive Index)
v = c / N1
Refractive Index of Core
c (meters/s)
v (speed through core, meters/s)
N1 = c / v

Fibre Latency

Latency (ms)
v (speed through core, meters/s)
d (Distance Km)
l = d / (v/1000)