# ls9 - class 9 tues march 4 in textbook chapter 15 More...

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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*(m2-m1)) F1/F2 = 10^(-0.4*(m1-m2)) handy approximation for small mags: if m2-m1 = 0.01, then F2/F1 = 0.991 --> diff of ~1% (0.9%) if m2-m1 = 0.10, then F2/F1 = 0.912 --> diff of ~10% (8.8%) if m2-m1 = 0.20, then F2/F1 = 0.832 --> diff of ~20% (16.8%) in other words, F2/F1 approx 1-(m2-m1). 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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ls9 - class 9 tues march 4 in textbook chapter 15 More...

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