front of it at the same brightness as a 100mcd LED with a viewing angle of
15 degrees, but will light a larger area, therefore is giving off more light
in total.
---
No.
100 millicandelas is the total light output, so the area illuminated
by the LED with the larger beamwidth will be dimmer.
Uhh... No...
Candelas aren't a measure of total light output. Candelas are a measure of
lumens per steradian (a steradian being a solid angle measurement). Lumens
are a measure of total light output adjusted for human eye sensitivity
towards different wavelengths. Human eyeballs are vastly more sensitive to
555nm green photons than they are to say red or blue photons for example.
So... A one lumen white light source should in theory be able to light up a
whole room to approximately an equal amount of brightness as perceived by a
human eye as a one lumen blue light source, as a one lumen green light
source, as a one lumen red light source, etc. The one lumen green light
source doesn't have to be as electrically efficient (in terms of total
photons produced per joule input) however since the human eye doesn't need
as many green photons to appear equally bright as other colors.
Unfortunately the vast majority of LED manufacturer's don't yet rate their
LED product's output in lumens, instead they usually provide intensity in
millicandelas and also include a "viewing angle" which is normally defined
as twice the angle of half intensity (or in other words two phi one-half).
Sometimes instead they might give you just the angle of half intensity
instead (especially in the case of infrared LEDs). This is a most
unfortunate state of affairs, because it precludes highly accurate and fair
comparisons between products.
Anyway, the OP's assumption was in fact correct. A 100mcd LED with a
viewing angle of 30 degrees *should* produce more total light output than a
100mcd LED with a viewing angle of 15 degrees. This doesn't absolutely
always have to be true however, since it depends on the beam profile, and it
also depends on how accurate and truthful the manufacturer's specifications
are. By playing with the beam profile, it is possible to make a 30 degree
100mcd LED produce less total light output than a 100mcd 15 degree LED,
without lying in any way on the specifications, but in most cases the 30
degree product should be superior.
If you want the most total light output and highest efficiency product, go
for LEDs that have high mcd ratings as well as large viewing angle ratings.
Unfortunately manufacturer's and especially distributors often make mistakes
on their advertising (usually because distributors don't have a clue what
any of the various units mean either), further muddling the issue and making
accurate direct performance comparisons even more difficult.