Monochromatic light shines on a diffraction grating with 8,600 lines uniformly distributed over 1.8 cm. The grating is illuminated using a laser of 630 nm wavelength. A diffraction pattern is formed on a screen located at 1.7 m away from the grating. (a) What is the angle of the first-order maximum of the 630-nm light incident upon the grating? (b) What is the separation on the screen between the first and the second order maxima? (c) What is the highest order maximum of 630-nm light that this diffraction can produce? Justify.
separation between adjacent slits (or) grating element,
d = 1.8*10^-2/8600
= 2.09*10^-6 m
lamda = 630 nm = 630*10^-9 m
R = 1.7 m
a) for first order maximum, d*sin(theta) = lamda
sin(theta) = lamda/d
= 630*10^-9/(2.09*10^-6)
= 0.301
theta = sin^-1(0.301)
= 17.5 degrees <<<<<<<---------------Answer
b) the separation on the screen between the first and the second order maxima = 2*lamda*R/d - lamda*R/d
= lamda*R/d
= 630*10^-9*1.7/(2.09*10^-6)
= 0.512 m <<<<<<<---------------Answer
c) for maximum n value,
d*sin(90) = n*lamda
==> n = d/lamda
= 2.09*10^-6/(633*10^-9)
= 3.3
= 3 <<<<<<<---------------Answer
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