1051-455-20073 Homework #6
Read P3§9 Coherence and P3§11 Frau nh of er Diffraction
Due 16 May 2008 (Th) —: Write up ONE lab of your choice in the “long format” (including abstract,
data, analysis, etc., as listed in the handout)
Due 8 May 2008 (Th) — Do the following problems; SHOW YOUR WORK
1. “White” light includes equal “amounts” of each wavelength in the interval 400 nm ≤λ≤700 nm.
(a) Determine the frequency bandwidth for this wavelength range
(b) Compute the associated coherence time and coherence length of white light.
2. The range of angular temporal frequencies by a light source is ∆ω:
(a) Find the expression for ∆ν
(b) Derive the expression for the corresponding linewidth ∆λ
(c) Derive the expression for the cohe rence le ngt h ∆of the source.
(d) Find the coherence length of a sodium arc that emits two narrow spectral lines:
ω1=3.195 ×1015 radians
sec
ω2=3.198 ×1015 radians
sec
(e) Find the coherence length of a He:Ne “greenie” laser with
ω1=3.171 ×1015 radians
sec
ω2=3.469 ×1015 radians
sec
3. Determine the linewidth in nanometers and in Hertz for laser light whose coherence length is 10 km if
the mean wavelength is 632.8nm (He:Ne)
4. Michelson found that the cadmium red line (λ0= 643.8nm) was the best available light source for
his interference experiment. With it, he could see fringes for optical path differences up to 300 mm.
Estimate the linewidth ∆λand coherence time ∆tof this light source.
5. A light source emits two wavelengths λ1and λ2. The light is incident upon a binary (composed of
regions that are perfectly transparent or perfectly opaque) f[x, y ]. The light then propagates to an
observation screen located at a very large distance Lfrom the object. Describe and give reasons for
the qualitative appearanceof the observed patterns for the following objects; you may also describe the
patterns quantitatively for extra credit.
(a) fa[x, y]is a single very small transparent aperture (“hole”)
(b) fb[x, y]consists of two apertures that are very narrow along the x−axis and infinitely long along
the y−axis and that are separated by dunits.
(c) fc[x, y]consists of an infinite number of apertures from part bthat are uniformly spaced at
increments of dunits.
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