An astronomer is calibrating a spectrometer that uses a dittraction grating to separate light in order of increasing wavelength (A, er and 1). She observes three distinct iirst-order spectral lines at the following respective angles @m (where m denotes order). 8, = 12.70, 8, = 14.2°, 0, = 14.9a (a) If the grating has 3,680 qrooves per centimeter, what wavelength (in nm) describes each of these spectral lines? at 8, - 12.70 24 - nm at 8, = 14.20 nm al 8, = 14.9° (b) At what angle (in degrees) would each of these lines be found in the second-order spectrum? for 2, for å 82 for 2. 82 =

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An astronomer is calibrating a spectrometer that uses a dittraction grating to separate light in order ot increasing wavelength (2,, 1e, and 1). She observes three distinct tirst-order
spectral lines at the following respective angles 0, (where m denotes order).
8, = 12.7°, 8, = 14.2°, 0, = 14.9c
(a) If the grating has 3,680 qrooves per centimeter, what wavelength (in nm) describes each of these spectral lines?
at 8, - 12.70
nm
at 6, = 14.2°
nm
al 8, = 14.9°
d =
(b) At what angle (in degrees) would each of these lines be found in the second-order spectrum?
for 2,
0, -
for å, 0,
for 2.
8, =
Transcribed Image Text:An astronomer is calibrating a spectrometer that uses a dittraction grating to separate light in order ot increasing wavelength (2,, 1e, and 1). She observes three distinct tirst-order spectral lines at the following respective angles 0, (where m denotes order). 8, = 12.7°, 8, = 14.2°, 0, = 14.9c (a) If the grating has 3,680 qrooves per centimeter, what wavelength (in nm) describes each of these spectral lines? at 8, - 12.70 nm at 6, = 14.2° nm al 8, = 14.9° d = (b) At what angle (in degrees) would each of these lines be found in the second-order spectrum? for 2, 0, - for å, 0, for 2. 8, =
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Step 1

Diffraction Grating

A diffraction grating is an optical instrument that is used to split a wave of light into many waves moving in different directions. It is used to observe the phenomena of diffraction.

A grating consists of a large number of slits in a very small region. If λ is the wavelength of light used and d is the distance between the two slits, then the condition for mth order maxima is

dsinθ=mλ

θ is the angle where the maxima are observed with respect to the horizontal.

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