Light of wavelength 523 +- 11 nm passes through an interference (diffraction) gr

Question

Light of wavelength 523 +- 11 nm passes through an interference (diffraction) grating that has 350 +- 10 slits/mm. Describe the pattern produced by the light passing through the grating. Use the wave model of light to predict mathematically the positions of all significant features of this pattern

Light of wavelength 523 ± 11 nm passes through an interference (diffraction) grating that has 350 ± 10 slits/mm. Describe the pattern produced by the light passing through the grating. Use the wave model of light to predict mathematically the positions of all significant features of this patterrn 1.

Explanation / Answer

for a multislit diffraction grating
for N lines per metre, the slitwidth is defined as a = 1/N m
now for a multislit diffraction grating with slit width a, and wavelength oflight lambda
the maximas are obtained at theta = n*lambda*N [ where theta is the angle wwith the horizontal where the maximas are found ]
given , lambda = 523+- 11 nm
N = 350+-10 slits per mm
so, maximas arte obtained at theta +- d(theta)
where d(theta)/theta = d(lambda)/lambda + d(N)/N

so, theta = n*350*10^-9*523000 = 0.18305 radians
d(theta)/0.18305 = 11/523 + 10/350 = 0.00908 rad

so the maximas would be observed at theta = 0.18305 +- 0.00908 radians, with decreasionjg intensity of subsequent maximas, but the distance between the maximas would remain a constant

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