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PHYS2125: OPTICS & RADIATION PHYSICS
THIRD OPTICS ASSIGNMENT, 2016
Due Date: Tuesday 24 May, 5:00 pm
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Problems on Material Optics
(Maximum marks are shown in brackets)
A common way of specifying the refractive index properties of glass used for optical
components is in terms of two numbers, a refractive index and a dispersion index.
Refractive indexes are measured at certain standard wavelengths, corresponding to
strong spectral line emissions from gases such as hydrogen, helium, cadmium and
mercury. The three most commonly used wavelengths are:
The refractive indexes at these wavelengths are designated nC, nd and nF respectively.
Dispersion is specified in terms of the Abbe value vd, defined by
n F nC
A very common type of glass is BK7, which has nd = 1.51680 and vd = 64.17
From this information, calculate an approximate value for the group refractive index
ng of BK7 at 588 nm.
What is the imaginary part of the index of refraction for a medium in which the
electric field amplitude of a 488 nm light beam is attenuated to 0.20 of its starting
value after travelling a distance of 50 nm in the medium? (Note that when the
wavelength of a light beam is quoted, it is always the wavelength in air unless
Under what conditions would the reflectance R and the transmittance T be equal to
each other at normal incidence at an interface? What would be the value of R and T
under these conditions?
For a material in thermal equilibrium at room temperature, T = 300 K, what is the ratio
of the upper to lower population density in a pair of states separated by an energy
difference corresponding to a wavelength of 633 nm?
(i) Calculate the values of the Einstein A and B coefficients for the case of a transition
at = 1.15 m with a lifetime of 120 ns (neon gas has a transition like this).
(ii) How large would the spectral radiant energy density at this wavelength have to be
to make the rate of stimulated emission be equal to the rate of spontaneous emission?
(iii) Suppose the radiant energy is supplied in the form of a parallel beam of light with
a cross-sectional area of 1.0 mm2. How much power would this beam have within a
spectral interval of 0.10 nm?
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