Question

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.

Answer 1

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