Question

# The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656...

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 500 lines per mm, and the light is observed on a screen 1.50 m behind the grating.

What is the distance between the first-order red and blue fringes?

?red = 656 nm
?blue = 486 nm
line density = 500 / mm
L = 1.5 m
d = 1 mm / 500 lines = 2?10-3 mm
m = 1

the positions can be determined by using the formula ?=sin-1(m?/d) & Ltan(?)=y
?red = sin-1(1??red/d) = sin-1(656 nm / 2?10-3 mm)
?red = 0.334186 rads = 19.14743°
yred=Ltan(?red) = (1.5 m)tan(19.14743°) = 0.521 m
?blue = sin-1(1??blue/d) = sin-1(486 nm / 2?10-3 mm)
?blue = 0.245457 rads = 14.06367°
yblue=Ltan(?blue) = (1.5 m)tan(14.06367°) = 0.376 m

so the blue fringe begins at 0.376 m and the red fringe begins at 0.521 m
the distance in between the fringes is yred-yblue = 0.145 m = 14.5 cm

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