Question

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14. A diffraction grating has 3000 lines/cm. Monochromatic yellow light (= 589 nm, i.e. 5.89 x 10 m) is incident on the grating. If this light can be seen in third order, calculate the angle at which it appears. If it cannot be seen in third order, show why not. (8 points)

Answer 1

For diffraction grating,
We have d×sin(x) = n×w ...(1)
Where d=width of one line
x=angle of diffraction
n=order of diffraction
w=wavelength of light used

As there are 3000 lines / cm
So width of one line d = 1cm/3000 = 3.33×10^-4 cm

= 3.33×10^-6m
Order of diffraction n = 3
And wavelength = 5.89×10^-7m

So putting values of d,n and w in equation (1) we have,
{ 3.33×10^-6 } × sin(x) = 3 ×{ 5.89×10^-7 }
i.e. sinx = 1.767×10^-6/ 3.33×10^-6
i.e. sinx = 0.530
i.e. x = sin^{​​​​-1}(0.530) = 32.005°

Therefore the light can be seen in third order and it will be seen at an angle of 32.005°