1.i) Nick has two semi-infinite plates of glass (refractive index 1.5) which are initially in contact along a common plane. A monochromatic s-polarized plane wave of wavelength 0.5pm is incident on the common plane at an angle of 60 degrees relative to the normal. What is the transmissivity into the other piece of glass as a function of the separation of the glass plates, if their surfaces remain parallel?

ii) Approximating the response of a metal by that of free electrons with plasma frequency w_p = 5 x 10¹⁵ and damping coefficient 7 = 1 x 10"r¹, for which wavelengths is the reflectivity for p-polarized light >99% and at what wavelength does the reflectivity minimum occur if the metal surface is flat and surrounded by air?

iii)Zach allows a monochromatic plane light wave with wavelength 0.8 pm to be incident at 45 degrees on a perfect, low amplitude, infinite 1-D sinusoidal grating with period 5 microns. How many reflected plane wave components are generated?

2.i) Pisek has a sodium lamp which emits bright yellow light associated with the "d-doublet". The doublet consists of Lorentzian emission peaks centred at 588.995 nm and 589.592 nm with an (intensity) FWHM of 0.001 nm. If a Michelson interferometer is used to resolve these two emission peaks, what is the path length difference that will make the fringe visibility become 1/2 of its peak value?

ii) If a Fabry-Perot interferometer with nominal plate separation of 1 cm is used to resolve the two peaks according to the Rayleigh criterion, what is the identical, minimum reflectivity of the two mirrors?

3.i) Lukas's eye glasses are coated with an antireflection coating consisting of two quarter wavelength layers of MgF2 (71 = 1.38) and ZrO2 (n = 2.1). They provide minimum reflectivity at 0.6 microns. For normally incident light, do the glasses have <1% reflectivity at 400 nm? If the angle of incidence is 30 degrees and s-polarized light is incident, is the reflectivity < 1% for 600 nm?

ii) An infinitely thick multilayer system consists of thin films of thickness d but with refractive index that alternate between ni and n2 with Ini - n2I << n1. Show that such a system possesses at least one band of wavelengths for which the reflectivity is unity. Such as system is sometimes referred to as a 1-D photonic crystal and the reflection band, within which light cannot propagate in the material, is often referred to as the band-gap, by analogy with the band gap electrons may possess in a crystalline solid. In terms of the refractive indices and d what is the centre wavelength of the longest wavelength reflection band? What is the width (in wavelength) of this reflection band? Hint: Rather than take a transfer matrix approach to this, you may want to consider what form propagating and non-progating solutions to the wave equation take.