2. A diffraction grating with 500 lines/mm is used to separate the two yellow li
ID: 1453741 • Letter: 2
Question
2. A diffraction grating with 500 lines/mm is used to separate the two yellow lines of sodium with = 588.995 nm and ’ = 589.592 nm. Determine the grating constant d. Determine the angular position and ’ in first order for the two lines. If the lines are viewed on a screen 2.00 m from the grating plane, what is the separation y between the two lines on the screen. Your answer for y needs at least 3 significant figures so do not round off the grating constant and wavelength values. 2. A diffraction grating with 500 lines/mm is used to separate the two yellow lines of sodium with = 588.995 nm and ’ = 589.592 nm. Determine the grating constant d. Determine the angular position and ’ in first order for the two lines. If the lines are viewed on a screen 2.00 m from the grating plane, what is the separation y between the two lines on the screen. Your answer for y needs at least 3 significant figures so do not round off the grating constant and wavelength values. 2. A diffraction grating with 500 lines/mm is used to separate the two yellow lines of sodium with = 588.995 nm and ’ = 589.592 nm. Determine the grating constant d. Determine the angular position and ’ in first order for the two lines. If the lines are viewed on a screen 2.00 m from the grating plane, what is the separation y between the two lines on the screen. Your answer for y needs at least 3 significant figures so do not round off the grating constant and wavelength values.Explanation / Answer
N =500 lines/mm
grating constant N = 500000 lines/m
d =1/N = 1/500000 lines/m
= 588.995 nm, n=1
dsin = n
sin = (588.995*10^-9)*(500000)
=17.13 degrees
'= 589.592 nm
dsin' = n
sin = (589.592*10^-9)*(500000)
' =17.145 degrees
D = 2 m
Y = nD/d
y = D/d (' - )
= (2*500000)(589.592-588.995)*10^-9
y = 0.597 mm
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