For your science fair project you need to design a diffractiongrating that will

Question

For your science fair project you need to design a diffractiongrating that will disperse the visible spectrum (400-700nm) over 30 degrees in first order. How many lines per millimeter does your grating need? What is the first-order diffraction angle of light from asodium lamp (wavelength = 589nm)? For your science fair project you need to design a diffractiongrating that will disperse the visible spectrum (400-700nm) over 30 degrees in first order. How many lines per millimeter does your grating need? What is the first-order diffraction angle of light from asodium lamp (wavelength = 589nm)?

Explanation / Answer

first find the spacing   d using     = dsin . So you know       400 = d sin1    and   700 = d sin2 . And    2 -1 = 30 degrees . How do you solve for d? It is very tricky, and cannot bedone algebraically. You have to crunch numbers (i.e. trial anderror... using a spreadsheet) to get it. . I just did this and got:      d =812.5 nanometers =   0.8125 x 10-3 mm . Note: for this d,   the two angles are 29.49 and 59.49 . So the spacing is     1 / 0.8125 x10-3 =    1231 lines per mm . The angle for the sodium light then is .      589 = 812.5sin      = 46.46 degrees . The angle for the sodium light then is .      589 = 812.5sin      = 46.46 degrees

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