4500PR06 - Rowland Circle Grating Spectrometer A Rowland...

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Unformatted text preview: Rowland Circle Grating Spectrometer A Rowland circle grating spectrometer is to be used in an astronomical applica— tion. Visible light from a stellar object is to be analyzed. A concave grating of radius Rgmting disperses light from a slit into focused spectra. These spectra are focused along the circumference of the Rowland circle whose diameter is equal to Rgmting. Depend- ing on the period of the grating, multiple diffracted orders may be formed. An example Rowland circle grating spectrometer is shown in the figure. Third order spectrum Second order 5’0""? spectrum First order spectrum Central image The visible spectrum is often taken to be from /\ = 400 nm to A = 700 nm. The particu- lar Rowland circle grating spectrometer has a grating of period of 1, 700 nm and a radius of curvature of 1.00 m. It is to be used in air with an angle of incidence of 45° as shown in the figure. Also as shown in the figure, the second order spectrum and the third order spectrum overlap. Calculate, showing all work, the range of wavelengths in the second order and third order spectra overlap. Express your answers in nanometers accurately to within 0.1 nm. Put your final answers in the spaces provided. Second-order visible wavelengths that overlap with third-order wavelengths nm < A2nd order < nm Third—order visible wavelengths that overlap with second-order wavelengths nm < A3rd order < nm On the drawing, label the angular locations of the above four wavelengths. Rowland Circle Grating. Spectrometer A = 1700nm Rgmfing = 1.00m 19' = 45° 11.1 = 1.000 Visible spectrum 400 nm < A < 700 nm Backward-diffracted order grating equations A - .r - .r _ -_ .3an + 33116; H 2A and so . ,r . ,r A2 smfi + 3271.02 = 2— A sinG’ + sinflf; z 3% a; = as therefore A2 - r A3 - I 2— — = — — A smfl 3 A smfl 2A2 = 3A3 A2 = %A3 = €400nm = 600nm A3 = %)\2 = %700nm = 466.67nm < order < ...
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4500PR06 - Rowland Circle Grating Spectrometer A Rowland...

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