FREQUENTLY ASKED QUESTIONS
February 8, 2012
Content Questions
How do we use the formula
I
ν
, where it’s all differentials?
The formula for
I
ν
, the specific intensity, is a
distribution
(sometimes called
a “differential distribution”): this is a very important kind of function that
is used often in science and engineering.
I think the best way to think of a distribution
f
(
x
) =
dn
(
x
)
dx
is as a
his
togram
, for which the bins are taken to be infinitesimally small. First think
of a histogram, with
M
bins of finite size Δ
x
i
. You have a total of
N
“items”
(people, photons, chunks of energy, gallons of water, whatever) to be dis
tributed among the bins. Bin
i
has
n
i
of them, such that Σ
M
i
=1
n
i
=
N
. So
what the histogram describes is “number of items per Δ
x
” as a function of
x
, or, for a continuous quantity, “amount of stuff per Δ
x
” as a function of
x
. In the limit that the bin width gets infinitesimally small, Δ
x
→
dx
, the
distribution can be described as
dn
dx
.
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 Spring '08
 Kruse,M
 Physics, Book of Optics, Solid angle, plate scale

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