Question

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.

Part A What is the spacing between slits of the grating?

Answer 1

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