A helium-neon laser (λ=633nm) illuminates a diffraction grating. The distance between the two m=1 bright fringes is 30 cm on a screen 1.5 m behind the grating.
What is the spacing between slits of the grating?
condition for bright fringe in diffraction
a*sintheta = (m + 1/2 ) *lambda
m = 1 , 2 , 3
for small angle
sintheta = tantheta = y/R
a*y/R = (m + 1/2 ) *lambda
y = (m + 1/2 ) *lambda*R/a
for m = 1
y1 = (3/2)*lambda*R/a
distance between two m = 1 bright fringes , d = 2*y1
given d = 30 cm = 0.3 m
R = 1.5 m
a = spacing between slits = ?
wavelength lambda = 633*10^-9 m
0.3 = 2*(3/2)*633*10^-9*1.5/a
spacing between slits a = 9.495*10^-6 m
DONE please check the answer. any doubts post in comment box
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