White light is sent through a diffraction grating spectrometer with slits separa

Question

White light is sent through a diffraction grating spectrometer with slits separated by 2.45 x 10-6 m; it breaks up into the colors of the rainbow. Almost everyone agrees that each color of the spectrum has its own range of wavelengths.

Your professor estimates of the range of wavelengths for each color are: red: 640 nm -720 nm; orange: 600 nm - 640 nm; yellow: 570 nm - 600 nm; green: 520 nm - 570 nm; blue: 460 nm - 520 nm

a ) Calculate the range of angles for each color produced by the spectrometer.

b ) The fluorescent lights in this room put out a green light of wavelength 546 nm. At which
angle will this line appear?

Explanation / Answer

Part A)

The formula that applies is sin(angle) = m(wavelength)/d, so...

For Red

sin(angle) = 1(640 X 10-9)/(2.45 X 10-6)

angle = 15.1o

Same formula but now use 720 X 10-9 for the wavelength

angle = 17.1o

So the range for Red is 15.1o - 17.1o

For Orange

You will do the exact same thing with those two wavelengths (600nm - 640nm) and get angles of

Orange = 14.2o - 15.1o

For Yellow

Wavelengths between 570 nm - 600 nm

Yellow = 13.5o - 14.2o

For Green

Wavelengths between 520 nm - 570 nm

Green = 12.3o - 13.5o

For Blue

Wavelengths between 460 nm - 520 nm

Blue = 10.8o - 12.30

Part B)

sin(angle) = (546 X 10-9)/(2.45 X 10-6)

Angle = 12.9o

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