Comments on: What is the minimum size telescope needed to resolve this binary? http://www.telescopebuyingguide.com/blog/what-is-the-minimum-size-telescope-needed-to-resolve-this-binary/ Thu, 09 Feb 2012 00:31:25 +0000 http://wordpress.org/?v=2.7 hourly 1 By: Mountainboy19682 http://www.telescopebuyingguide.com/blog/what-is-the-minimum-size-telescope-needed-to-resolve-this-binary/comment-page-1/#comment-2345 Mountainboy19682 Fri, 25 Dec 2009 11:41:28 +0000 http://www.telescopebuyingguide.com/blog/what-is-the-minimum-size-telescope-needed-to-resolve-this-binary/#comment-2345 Assuming that the telescope is of high quality construction, and that the atmospheric conditions are perfect for observations, then the resolution is limited by diffraction. Light passing through the lens interferes with itself creating a ring-shaped diffraction pattern, known as the Airy pattern, if the wavefront of the transmitted light is taken to be spherical or plane over the exit aperture. The result is a blurring of the image. An empirical diffraction limit is given by the Rayleigh criterion invented by Lord Rayleigh: The images of two different points are regarded as just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other. If the distance is greater, the two points are well resolved and if it is smaller, they are not resolved. Mathematically, this translates into: D=1.220 x w/sin r Where D is the diameter of the main mirror or lens w is the wavelength of the light r is the resolution required in radians In this case we have: w = 5000 Angstroms r = 0.4 arc seconds = 0.000111111 degrees = 1.93925 x 10^-06 radians sin r = 1.93925 x 10^-06 radians Therefore D= 1.220 x 5000 / 1.93925 x 10^-06 Angstroms D = 3,145,538,295 Angstroms D = 31.46 centimeters or about 12 inches.<a href="http://www.ifished.com"> Mountainboy19682</a> Assuming that the telescope is of high quality construction, and that the atmospheric conditions are perfect for observations, then the resolution is limited by diffraction.
Light passing through the lens interferes with itself creating a ring-shaped diffraction pattern, known as the Airy pattern, if the wavefront of the transmitted light is taken to be spherical or plane over the exit aperture. The result is a blurring of the image. An empirical diffraction limit is given by the Rayleigh criterion invented by Lord Rayleigh:

The images of two different points are regarded as just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other. If the distance is greater, the two points are well resolved and if it is smaller, they are not resolved. Mathematically, this translates into:

D=1.220 x w/sin r
Where D is the diameter of the main mirror or lens
w is the wavelength of the light
r is the resolution required in radians

In this case we have:
w = 5000 Angstroms
r = 0.4 arc seconds = 0.000111111 degrees = 1.93925 x 10^-06 radians
sin r = 1.93925 x 10^-06 radians

Therefore
D= 1.220 x 5000 / 1.93925 x 10^-06 Angstroms
D = 3,145,538,295 Angstroms
D = 31.46 centimeters
or about 12 inches. Mountainboy19682

]]> By: Miss Fantastic http://www.telescopebuyingguide.com/blog/what-is-the-minimum-size-telescope-needed-to-resolve-this-binary/comment-page-1/#comment-2344 Miss Fantastic Tue, 22 Dec 2009 02:42:01 +0000 http://www.telescopebuyingguide.com/blog/what-is-the-minimum-size-telescope-needed-to-resolve-this-binary/#comment-2344 The Raleigh Criterion for angular resolution is probably the limiting factor here. sin(theta)=1.22*(wavelength)/(diameter of aperture) Rerranging: Diameter=1.22*(wavelength)/(sin(theta)) =1.22*(5000e-10 m)/(sin(1.94e-6 radians)) =.31 meters in diameter<a href="http://www.promusicmall.com/accessories-12758"> Miss Fantastic</a> The Raleigh Criterion for angular resolution is probably the limiting factor here.

sin(theta)=1.22*(wavelength)/(diameter of aperture)
Rerranging:
Diameter=1.22*(wavelength)/(sin(theta))
=1.22*(5000e-10 m)/(sin(1.94e-6 radians))
=.31 meters in diameter Miss Fantastic

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