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class 9. tues march 4
in textbook: chapter 15
More about magnitudes.
important equations:
m2  m1 = 2.5*alog10( F2/F1 )
m2  m1 = 2.5*alog10( F1/F2 )
F1/F2 = 10^(0.4*(m2m1))
F1/F2 = 10^(0.4*(m1m2))
handy approximation for small mags:
if m2m1 = 0.01, then F2/F1 = 0.991
> diff of ~1%
(0.9%)
if m2m1 = 0.10, then F2/F1 = 0.912
> diff of ~10%
(8.8%)
if m2m1 = 0.20, then F2/F1 = 0.832
> diff of ~20%
(16.8%)
in other words, F2/F1 approx 1(m2m1).
but not for big diffs in mag.
typical numbers:
Sun 26.7
Full Moon 12
Venus brightest 4
Sirius 1.5
Polaris 2.0
faintest you can see in really dark place  6, possibly 7 if you're keen.
faintest possible with optical telescopes  about 29 or 30.
What sort of range is that?
30  26.7 = 2.5*alog10(F2/F1) =>
F2/F1 = 4.8e22. large dynamic range.
specific wavelengths  handout #17. a magnitude must be specified
at a given wavelength  even if that wvln is 'visual' or 'photographic'.
in principle you could measure magnitudes at a bunch of
random wvlns  but for ease in comparison we have these standard ones.
Often these std wvlns will be called 'bands' or 'filters' because
you stick a filter in front of your camera to only let thru
light of the appropriate wvln.
So what is 'bandpass' = 'passband' = 'bandwidth' ? Your detector
detects wvln of not just a single wvln  that's very hard to
do engr wise. You actually detect a bunch of wavelengths.
for various filters. you see this a little bit on #17 but here's
a better representation of both vis and IR.
Each filter has some 'effective' wavelength that it corresponds to,
but you should know that photons of sevearl wvlns are actually
being recorded.
So how would you predict what sort of flux you'd get through your
filter? Or more generally  when you're at the telescope, what
you collect are photons, some number of photons N. How does
that related to the flux density F_lambda(lambda)?
Your filter has a response function of R(lambda). So what you
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 Spring '09
 Fernandez
 Astronomy

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