PDA

View Full Version : Apparent magnitude



George
2006-Aug-17, 10:34 PM
To the eye, is the apparent brightness of a dimmer star, that is one magnitude less than another, about 1/2 that of the brighter star? Does a star of mag. 1 appear 4x brighter (2x2) than a mag. 3 star?

I found only one site that mentions this when this all happened in the days of Hipparchus. Normally I read he scaled them from 1 to 6, then later we discovered the log relationship; but, no mention if the appearance of one to another is 2x more for the next brighter.

It makes sense that it might be true since our eye's are logarithmetic. But do our eyes (retinex) respond to a 2.51 base?

hhEb09'1
2006-Aug-17, 10:40 PM
He just took the brightest and the dimmest, and made five intervals between them--one for each finger. :)

grant hutchison
2006-Aug-17, 11:01 PM
The logarithm base has no particular relevance to perception. We might have ended up with some other base if Hipparchus had chosen to use more or fewer intervals, or if the span from his brightest to his dimmest rating hadn't turned out to be close enough to 100-fold to tempt Pogson into formalizing by making the ratio precise.

Grant Hutchison

George
2006-Aug-17, 11:22 PM
Thanks Grant, that seems to match all but one site on the web.

So, it would be very difficult to state with any real likelyhood that a star might look twice as bright, or other figure, as another star. It is too subjective.

George
2006-Aug-17, 11:23 PM
He just took the brightest and the dimmest, and made five intervals between them--one for each finger. :)
Hmmm...So that's why zero took so long to get here. ;)

hhEb09'1
2006-Aug-17, 11:39 PM
So, it would be very difficult to state with any real likelyhood that a star might look twice as bright, or other figure, as another star. It is too subjective.I dunno. There are a lot of psychological studies on levels of perception--remember, that is similar to the way the decibel scale was established. They just took an integrated generalization of the individual perceptions, however varied and subjective each of them were.

George
2006-Aug-17, 11:45 PM
Using the audio scale is a good analogy. When do we ever say something is twice as loud?

grant hutchison
2006-Aug-17, 11:55 PM
The trouble with "twice as bright" is that it implies an internal assessment of "zero brightness": if zero moves, the brightness ratio alters. (Which is the problem encountered by people who talk about "twice the temperature" in Fahrenheit or Celsius). Since our visual threshold is so variable, depending on adaptation, it's difficult to know how we could make an assessment of brightness ratios in any sort of reproducible manner.

Grant Hutchison

George
2006-Aug-18, 02:28 AM
Another good analogy. hhEb09'1's hearing analogy, your feel (of temp.) analogy, and the seeing issue leads me to suggest the Italian meal I just had might not have tasted twice as good as normal, though it seemed to, nor did it smell half as bad as some. No wonder mankind was a little slow with quantification. :)

Kaptain K
2006-Aug-18, 05:14 PM
Using the audio scale is a good analogy. When do we ever say something is twice as loud?
The generally accepted relationship is that something sounds twice as loud when the SPL (sound pressure level) increases by 10dB, which requires a tenfold increase in power.

George
2006-Aug-18, 10:48 PM
I wonder, though, if this isn't more subjective than we think. Can a drummer actually play twice as loud as normal if asked (even when measured on the db scale)? [Of course, we all know they can never play 1/2 as loud, if asked. :)]

grant hutchison
2006-Aug-18, 11:08 PM
There's a nice reference source here (http://www.phys.unsw.edu.au/~jw/dB.html), walking us through the phon and the sone (which bear something of the same relationship to the decibel as the lux does to the watt per square metre).
I find it interesting that people can be at all consistent about "twice as loud": it's not something I seem to be able to imagine, although that may just reflect a complete absence of musical training [or, indeed, exposure :sad:] at an early age. Is this reproducible and internally consistent to levels like, for instance, "a hundred times as loud"?

But I have spent a bit of time under starlit dark skies from an early age, and I certainly don't get a sense of doubling brightness with a single-magnitude difference. Like Hipparchus, I seem to have a sense of equal "increments", in some vague way that seems linear, as magnitudes decrease.

Grant Hutchison

Wolverine
2006-Aug-18, 11:35 PM
I wonder, though, if this isn't more subjective than we think. Can a drummer actually play twice as loud as normal if asked (even when measured on the db scale)? [Of course, we all know they can never play 1/2 as loud, if asked. :)]

You could try putting a piece of sheet music in front of them. Although, that might lower the output to 0dB in many cases.

George
2006-Aug-18, 11:48 PM
You could try putting a piece of sheet music in front of them. Although, that might lower the output to 0dB in many cases.
I've tried that. Their stick velocity far exceeds the fall rate of the sheet onto their drum. However, if it has words on it, they will keep it and ignore the rest. If you do it, just be sure you do want them to sing! :)

George
2006-Aug-18, 11:56 PM
There's a nice reference source here (http://www.phys.unsw.edu.au/~jw/dB.html), walking us through the phon and the sone (which bear something of the same relationship to the decibel as the lux does to the watt per square metre).

"The sone is derived from psychophysical measurements which involved volunteers adjusting sounds until they judge them to be twice as loud. This allows one to relate perceived loudness to phons. A sone is defined to be equal to 40 phons. Experimentally it was found that a 10 dB increase in sound level corresponds approximately to a perceived doubling of loudness."

I am surprised, too. I am still a little doubtful. I bet I could scatter their plot. :)