How do I compute the smallest angular size which can be resolved given the
size of the refractor, when no wavelengths are given?  Is there a simple
formula that does not involve wavelengths, or is there some standard
wavelength that is assumed if none is given?

Thanks for everyone's help in understanding this introductory astronomy
class.

"Robert"  wrote in message 
news:4817862b$0$25019$607ed4bc@cv.net...
> How do I compute the smallest angular size which can be resolved given the
> size of the refractor, when no wavelengths are given?  Is there a simple
> formula that does not involve wavelengths, or is there some standard
> wavelength that is assumed if none is given?
>
> Thanks for everyone's help in understanding this introductory astronomy
> class.
>
Well, what wavelength are you planning to use? You'll get better resolution 
in blue than in red from your mirror (a pedant would point out that your 
eyepiece may change that).

http://www.abdn.ac.uk/physics/px2009/diffsum.pdf

"newshound" wrote in message news:67pm7uF2ppqb6U1@mid.individual.net...
>
> "Robert"  wrote in message 
> news:4817862b$0$25019$607ed4bc@cv.net...
>> How do I compute the smallest angular size which can be resolved given 
>> the
>> size of the refractor, when no wavelengths are given?  Is there a simple
>> formula that does not involve wavelengths, or is there some standard
>> wavelength that is assumed if none is given?
>>
>> Thanks for everyone's help in understanding this introductory astronomy
>> class.
>>
> Well, what wavelength are you planning to use? You'll get better 
> resolution in blue than in red from your mirror (a pedant would point out 
> that your eyepiece may change that).
>
> http://www.abdn.ac.uk/physics/px2009/diffsum.pdf

The question as posed by the practice quiz was what is the smallest angular 
size for a refractor of size X inches?  No mention of a wavelength. That was 
what confused me because all the formulas I've seen for it involve 
wavelength, so what could they possibly mean?

Robert wrote:
> "newshound" wrote in message news:67pm7uF2ppqb6U1@mid.individual.net...
>> "Robert"  wrote in message 
>> news:4817862b$0$25019$607ed4bc@cv.net...
>>> How do I compute the smallest angular size which can be resolved given 
>>> the
>>> size of the refractor, when no wavelengths are given?  Is there a simple
>>> formula that does not involve wavelengths, or is there some standard
>>> wavelength that is assumed if none is given?
>>>
>>> Thanks for everyone's help in understanding this introductory astronomy
>>> class.
>>>
>> Well, what wavelength are you planning to use? You'll get better 
>> resolution in blue than in red from your mirror (a pedant would point out 
>> that your eyepiece may change that).
>>
>> http://www.abdn.ac.uk/physics/px2009/diffsum.pdf
> 
> The question as posed by the practice quiz was what is the smallest angular 
> size for a refractor of size X inches?  No mention of a wavelength. That was 
> what confused me because all the formulas I've seen for it involve 
> wavelength, so what could they possibly mean?

Sometimes you have to make sensible assumptions to be able to do physics 
or astronomy.

Visible light spans a range 340nm to 700nm roughly a factor of two but 
the eye is at its most sensitive in the mid green around 500-550nm so 
that is where most nominal calculations for resolution are done.

You can have a quick and dirty formula that doesn't explicitly involve 
wavelength on the implied assumption of visible light that is something 
like for example

Resolution in arsec = 5 / aperture in inches
or in metric (125/ aperture in mm)

All this is doing is incorporating the "constants" of proportionality 
and measurement units into a single memorable number.
See Wikipedia for more (exact number depends on chosen wavelength).

BTW Something is wrong with the astronomy course if this isn't 
immediately obvious from the lectures or coursework.

Regards,
Martin Brown
** Posted from http://www.teranews.com **

Hi

"newshound"  wrote in message
news:67pm7uF2ppqb6U1@mid.individual.net...
>
> "Robert"  wrote in message
> news:4817862b$0$25019$607ed4bc@cv.net...
> > How do I compute the smallest angular size which can be resolved given
the
> > size of the refractor, when no wavelengths are given?
> >
> Well, what wavelength are you planning to use? You'll get better
resolution
> in blue than in red from your mirror (a pedant would point out that your
> eyepiece may change that).

Sorry, but a pedant would point out that a refractor wouldn't have a mirror
in it.

Robert, try asking this on the ATM list ( http://www.atmlist.net ) They are
a knowledgeable and friendly bunch who would help you with this.

Neil

"Martin Brown" wrote in message 
news:6061b$481821c7$20584@news.teranews.com...
> BTW Something is wrong with the astronomy course if this isn't immediately 
> obvious from the lectures or coursework.

You bet! Some professors are just simply bad teachers. They misinterpret 
their obtuseness for being "challenging".

On Apr 29, 2:33 pm, "Robert"  wrote:
<snip> How do I compute the smallest angular size which can
> be resolved given the size of the refractor, when no
> wavelengths are given?

You should state the assumed wavelength that you applied.  Two common
choices include:

1) Dawes original assumption of two equal blue/white binaries at 460nm
wavelength (blue/white light).

2) Rayleigh's criteria that assumes 550nm yellow light.

Depending on the fiducial wavelength used, summary equations for
Dawes' and Rayleigh's criterias will vary slightly between any two
astronomy texts or books.

Another common wavelength that I have seen assumed in astronomy texts
is 500nm.

The common form of equation for these resolution criteria is based on
the angular size of the Airy disk, taken at:

A_radians = 2.44 * lambda / D  Eq. 1 where D (aperture) and lambda
(wavelength) are in the same units of measurement.

A_arcsecs = A_radians * 360/2pi() * 60 * 60 Eq. 2

The easiest common length basis for lambda and D is meters.  So lambda
- wavelength in nanometers - and aperture D in millimeters are
converted using:

D_meter = D_mm / 1000#  Eq. 3
lambda_meter = (lambda_nanometers * (10# ^ -9#)) Eq. 4

Dawes criteria states that two equal blue/white doubles in a 1 inch
aperture can be split when they are separated by 1/2 the Airy disk
size.

Collecting all the above terms and dividing by 1/2 in the aperture
units of millimeters gives:

Dawes criteria = 116 / D_mm  at 460nm  Eq. 5

Dawes criteria for a one inch aperture is:

4.56 arcsecs (per inch of aperture) = 116 / 25.4 mm

This is the most common statement of Dawes criteria - that the minimum
resolution of a telescope is 4.56 arcsecs per inch of aperture.

Rayleigh's criteria is similar but is based on 550nm light and reduces
to:

Rayleigh's criteria = 138 / D_mm at 550nm  Eq. 6

5.45 arcsecs (per inch of aperture) = 138 / 25.4 mm (per inch of
aperture)

This is the most common statement of Rayleigh's criteria - that the
minimum resolution of a telescope is 5.45 arcsecs per inch of
aperture.

The best wavelength value to use, where the wavelength is not
specified, depends on your stated purpose.  If you want a stringent
resolution test based on a common easily identified OB class equal
magnitude doubles - 460nm would be the best choice.  If you are
talking in generalities regarding the most commonly encountered visual
observing condictions - 550nm or 500nm - might be a better choice.  If
you are imaging with a CCD camera through a R or near infrared
bandpass I filter, 656nm might be the best choice.

The take-away point is that there a number of variants of the
simplified equations for Dawes, Rayleigh and/or Sparrow's criterias
floating around in textbooks, astronomy books and on the internet.
Most of the variations can be attributed to slightly different
selections of the fiducial wavelength.

- Canopus56

P.S. - A good practice exercise is to see if you can use Eq.s 1-4 to
derive Eqs. 5 and 6 in a spreadsheet.

wrote in message news:579a7f2a-ec38-4d6b-a820-
8477536a96f1@m3g2000hsc.googlegroups.com
> On Apr 29, 2:33 pm, "Robert"  wrote:
> <snip> How do I compute the smallest angular size which can
> > be resolved given the size of the refractor, when no
> > wavelengths are given?
>
> You should state the assumed wavelength that you applied.  Two common
> choices include:
>
> 1) Dawes original assumption of two equal blue/white binaries at 460nm
> wavelength (blue/white light).
>
> 2) Rayleigh's criteria that assumes 550nm yellow light.
>
> Depending on the fiducial wavelength used, summary equations for
> Dawes' and Rayleigh's criterias will vary slightly between any two
> astronomy texts or books.
>
> Another common wavelength that I have seen assumed in astronomy texts
> is 500nm.
>
> The common form of equation for these resolution criteria is based on
> the angular size of the Airy disk, taken at:
>
> A_radians = 2.44 * lambda / D  Eq. 1 where D (aperture) and lambda
> (wavelength) are in the same units of measurement.
>
> A_arcsecs = A_radians * 360/2pi() * 60 * 60 Eq. 2
>
> The easiest common length basis for lambda and D is meters.  So lambda
> - wavelength in nanometers - and aperture D in millimeters are
> converted using:
>
> D_meter = D_mm / 1000#  Eq. 3
> lambda_meter = (lambda_nanometers * (10# ^ -9#)) Eq. 4
>
> Dawes criteria states that two equal blue/white doubles in a 1 inch
> aperture can be split when they are separated by 1/2 the Airy disk
> size.
>
> Collecting all the above terms and dividing by 1/2 in the aperture
> units of millimeters gives:
>
> Dawes criteria = 116 / D_mm  at 460nm  Eq. 5
>
> Dawes criteria for a one inch aperture is:
>
> 4.56 arcsecs (per inch of aperture) = 116 / 25.4 mm
>
> This is the most common statement of Dawes criteria - that the minimum
> resolution of a telescope is 4.56 arcsecs per inch of aperture.
>
> Rayleigh's criteria is similar but is based on 550nm light and reduces
> to:
>
> Rayleigh's criteria = 138 / D_mm at 550nm  Eq. 6
>
> 5.45 arcsecs (per inch of aperture) = 138 / 25.4 mm (per inch of
> aperture)
>
> This is the most common statement of Rayleigh's criteria - that the
> minimum resolution of a telescope is 5.45 arcsecs per inch of
> aperture.
>
> The best wavelength value to use, where the wavelength is not
> specified, depends on your stated purpose.  If you want a stringent
> resolution test based on a common easily identified OB class equal
> magnitude doubles - 460nm would be the best choice.  If you are
> talking in generalities regarding the most commonly encountered visual
> observing condictions - 550nm or 500nm - might be a better choice.  If
> you are imaging with a CCD camera through a R or near infrared
> bandpass I filter, 656nm might be the best choice.
>
> The take-away point is that there a number of variants of the
> simplified equations for Dawes, Rayleigh and/or Sparrow's criterias
> floating around in textbooks, astronomy books and on the internet.
> Most of the variations can be attributed to slightly different
> selections of the fiducial wavelength.
>
> - Canopus56
>
> P.S. - A good practice exercise is to see if you can use Eq.s 1-4 to
> derive Eqs. 5 and 6 in a spreadsheet.

The Dawes limit. Put simply, (4.56/d) sec, d in inches. It's an empirical
formula, so the wavelength doesn't matter. Dawes worked it out assuming
yellow stars of magnitude 6.