Questions about IRC

[GreenXenon]

Hi:

Far-Infrared Radiation [Infrared C band] is from 3,000 to 1,000,000
nm. What is the middle-most wavelength of FIR?

Here is what I got.

1,000,000 nm - 3,000 nm = 997,000 nm

997000/2 = 498,500 nm

498,500 nm + 3,000 nm = 501,500 nm

Am I correct?

[[Mod. note -- There's more than one way to define "middle". You have
used the arithmetic mean. Another possibility would be the geometric
mean, which would give around 55,000 nm. There are other definitions
of "middle" possible, but arithmetic and geometric are probably the
most commonly-used... -- jt]]

If so, then I have an additional question. What is the most efficient
way to generate monochromatic 501,500 nm light without generating
light of any other wavelengths?


Thanx

[Roland Franzius]

GreenXenon schrieb:
> Hi:
>
> Far-Infrared Radiation [Infrared C band] is from 3,000 to 1,000,000
> nm. What is the middle-most wavelength of FIR?
>
> Here is what I got.
>
> 1,000,000 nm - 3,000 nm = 997,000 nm
>
> 997000/2 = 498,500 nm
>
> 498,500 nm + 3,000 nm = 501,500 nm
>
> Am I correct?

More common is the formula 1/2 (1,000,000+3,000). Same result of course.

Phyically one prefers the inverse of the mean of the inverses

1/(1/1,000,000 + 1/3,000) = 2912,621359223300970873786407767

because wave numbers and frequencies are more likely to produce means
compared to wavelengths and cycle times.

>
> [[Mod. note -- There's more than one way to define "middle". You have
> used the arithmetic mean. Another possibility would be the geometric
> mean, which would give around 55,000 nm. There are other definitions
> of "middle" possible, but arithmetic and geometric are probably the
> most commonly-used... -- jt]]
>
> If so, then I have an additional question. What is the most efficient
> way to generate monochromatic 501,500 nm light without generating
> light of any other wavelengths?


Something like cryogenic masers?

http://tycho.usno.navy.mil/ptti/1992/Vol%2024_22.pdf

--

Roland Franzius

[John Polasek]

On Sun, 08 Feb 2009 18:13:34 EST, GreenXenon <glucegen1x@gmail.com>
wrote:

>Hi:
>
>Far-Infrared Radiation [Infrared C band] is from 3,000 to 1,000,000
>nm. What is the middle-most wavelength of FIR?
>
>Here is what I got.
>
>1,000,000 nm - 3,000 nm = 997,000 nm
>
>997000/2 = 498,500 nm
>
>498,500 nm + 3,000 nm = 501,500 nm
>
>Am I correct?
>
>[[Mod. note -- There's more than one way to define "middle". You have
>used the arithmetic mean. Another possibility would be the geometric
>mean, which would give around 55,000 nm. There are other definitions
>of "middle" possible, but arithmetic and geometric are probably the
>most commonly-used... -- jt]]
>
>If so, then I have an additional question. What is the most efficient
>way to generate monochromatic 501,500 nm light without generating
>light of any other wavelengths?
>
>
>Thanx
Think about finding your wavelength using the mean frequency as the
metric, since frequency is, after all, a measure of energy.

The answer is a surprise. For a quick answer you can take the
reciprocal of the mean of the sum of the reciprocals which is equal to
twice the product divided by sum, and the result is 5982 nm.

The mean WL based on frequency/energy considerations is 5982 nm.

Recognize that your calculation of the mean gives unwarranted weight
to the 1,000,000 nm end (and the 100,000 end, etc.) , where the
frequency and energy are essentially zero, by comparison with the
short end.

John Polasek