Spectrographs
This problem set is designed for astronomy to help the student, teacher, and researcher understand the inner workings of a spectrograph.
ContentsEvaluation

Spectrography[edit]
Def. a "machine for recording spectra, producing spectrograms"^{[1]} is called a spectrograph.
Def. a "visual representation of the spectrum of a celestial body's radiation"^{[2]} is called a spectrogram.
A "prism is a transparent optical element with flat, polished surfaces that refract light [over a range of wavelengths]. At least two of the flat surfaces must have an angle [α] between them. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use "prism" usually refers to this type."^{[3]}
"Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface. For the prism shown at right, the indicated angles are given by"^{[3]}
 '"`UNIQpostMath00000005QINU`"'.
"For a prism in air '"`UNIQpostMath00000006QINU`"'. Defining '"`UNIQpostMath00000007QINU`"', the deviation angle '"`UNIQpostMath00000008QINU`"' is given by"^{[3]}
 '"`UNIQpostMath00000009QINU`"'
"If the angle of incidence '"`UNIQpostMath0000000AQINU`"' and prism apex angle '"`UNIQpostMath0000000BQINU`"' are both small, '"`UNIQpostMath0000000CQINU`"' and '"`UNIQpostMath0000000DQINU`"' if the angles are expressed in radians. This allows the nonlinear equation in the deviation angle '"`UNIQpostMath0000000EQINU`"' to be approximated by"^{[3]}
 '"`UNIQpostMath0000000FQINU`"'
"The deviation angle depends on wavelength through n, so for a thin prism the deviation angle varies with wavelength according to"^{[3]}
 '"`UNIQpostMath00000010QINU`"'.
Problem 1[edit]
The image at the top of this resource appears to have a deviation angle of 45°. The detector may be about 4 cm from the prism. Using a refractive index n = 1.732 and a representative wavelength for the optical colors calculate the width of each wavelength channel and the total detector width to capture the incoming photons. Use an apex angle of 35°.
Problem 2[edit]
Let the deviation angle be 30°, the detector distance be half a meter with the same refractive index and apex angle of 37.5°.
For the optical colors calculate the width of each wavelength channel and the total detector width to capture the incoming photons.
Problem 3[edit]
Using the configuration of Problem 2 and assuming a prism for Xrays and gamma rays existed, calculate the width of each wavelength channel, for five representative wavelengths of each, and the total detector width to capture the incoming photons.
Problem 4[edit]
Using the configuration of Problem 1 and representative wavelengths for each of the infrared bands described in infrared astronomy, calculate the width of each wavelength channel and the total detector width to capture the incoming photons.
Problem 5[edit]
Using each configuration of the problems above and representative wavelengths for submillimeter, microwave, and radio waves, calculate the width of each wavelength channel and the total detector width to capture the incoming photons.
Hypotheses[edit]
 Amateur astronomers may be able to build or buy a spectrograph.
 See also: Control groups, Proof of concept, and Proof of technology
See also[edit]
References[edit]
 ↑ Lua error in Module:Citation/CS1 at line 3505: bad argument #1 to 'pairs' (table expected, got nil).
 ↑ Lua error in Module:Citation/CS1 at line 3505: bad argument #1 to 'pairs' (table expected, got nil).
 ↑ ^{3.0} ^{3.1} ^{3.2} ^{3.3} ^{3.4} Lua error in Module:Citation/CS1 at line 3505: bad argument #1 to 'pairs' (table expected, got nil).
External links[edit]
 Bing Advanced search
 Google Books
 Google scholar Advanced Scholar Search
 International Astronomical Union
 JSTOR
 Lycos search
 NASA/IPAC Extragalactic Database  NED
 NASA's National Space Science Data Center
 Office of Scientific & Technical Information
 Questia  The Online Library of Books and Journals
 SAGE journals online
 The SAO/NASA Astrophysics Data System
 Scirus for scientific information only advanced search
 SDSS Quick Look tool: SkyServer
 SIMBAD Astronomical Database
 SIMBAD Web interface, Harvard alternate
 Spacecraft Query at NASA.
 SpringerLink
 Taylor & Francis Online
 Universal coordinate converter
 Yahoo Advanced Web Search
{{Astronomy resources}}
{{Charge ontology}}
{{Flight resources}}
{{Principles of radiation astronomy}}
{{Repellor vehicle}}
{{Technology resources}}