Diffraction Problems-2 (Double slit & Grating)
1
A certain grating has 104 slits with a spacing of d = 2100 nm. It is illuminated with yellow
sodium light ( = 589 nm). Find (a) the angular position of all principal maxima observed
and (b) the angular width of the largest order maximum.
2.
A grating has 315 rulings / mm. For what wavelengths in the visible spectrum can fifthorder diffraction be observed?
3.
Given a grating with 400 rulings/mm, how many orders of the entire visible spectrum
(400-700nm) can be produced?
4.
A diffraction grating has 1.20 X 104 rulings uniformly spaced over a width W = 2.50cm. It
is illuminated at normal incidence by yellow light from a sodium vapor lamp. This light
contains two closely spaced lines of wavelengths 589.0 nm and 589.59 nm. (a) At what
angle does the first maximum occur for the first of these wavelengths? (b) What is the
angular separation between these two lines (1st order)? (c) How close in wavelength can
two lines be (in first order) and still be resolved by this grating? (d) How many rulings can
a grating have and just resolve the sodium doublet line?
A grating has 9600 lines uniformly spaced over a width 3cm and is illuminated by
mercury light.
a) What is the expected dispersion in the third order, in the vicinity of intense
green line ( = 546nm)?
b) What is the resolving power of this grating in the fifth order?
c) What is the wavelength difference that can be resolved in the 5th order.
5.
6.
7.
8.
The sodium doublet in the spectrum of sodium is a pair of lines with wavelengths 589.0
and 589.6 nm. Calculate the minimum number of rulings in a grating needed to resolve
this doublet in the second-order spectrum.
In a particular grating, the sodium doublet is viewed in third order at 10.2 to the normal
and is barely resolved. Find (a) the ruling spacing and (b) the total width of grating.
Calculate, approximately, the relative intensities of the maxima in the single slit
Fraunhofer diffraction pattern.