INTRO:
The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm(red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 510lines/mm , and the light is observed on a screen 1.3m behind the grating.
Part A:
What is the distance between the first-order red and blue fringes?
Express your answer to two significant figures and include the appropriate units.
SOLUTION:
givens:
λred = 656 nm
λblue = 486 nm
line density = 510 / mm
L = 1.3 m
d = 1 mm / 510 lines = 1.961⋅10-3 mm
m = 1
the positions can be determined by using the formula θ=sin-1(mλ/d) & Ltan(θ)=y
θred = sin-1(1⋅λred/d) = sin-1(656 nm / 1.961⋅10-3 mm)
θred = 0.341099 rads = 19.5435°
yred=Ltan(θred) = (1.3 m)tan(19.5435°) = 0.462 m
θblue = sin-1(1⋅λblue/d) = sin-1(486 nm / 1.961⋅10-3 mm)
θblue = 0.250443 rads = 14.349°
yblue=Ltan(θblue) = (1.3 m)tan(14.349°) = 0.333 m
so the blue fringe begins at 0.333 m and the red fringe begins at 0.462 m
the distance in between the fringes is yred-yblue = 0.129 m = 13 cm
You don't convert d to meters?
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