ELEC425/6261
Assignment 1
1. Refractive index
(a) Consider light of free-space wavelength 1300 nm traveling in pure silica medium. Calculate
the phase velocity and group velocity of light in this medium. Is the group velocity ever greater
than the phase velocity?
(b) What is the Brewster angle (the polarization angle p) and the critical angle (c) for total
internal reflection when the light wave traveling in this silica medium is incident on a silica/air
interface. What happens at the polarization angle?
(c) What is the reflection coefficient and reflectance at normal incidence when the light beam
traveling in the silica medium is incident on a silica/air interface?
(d) What is the reflection coefficient and reflectance at normal incidence when a light beam
traveling in air is incident on an air/silica interface? How do these compare with part (c) and
what is your conclusion?
2. Reflection at glass-glass and air-glass interfaces: A ray of light which is traveling in a
glass medium of refractive index n1 = 1.460 becomes incident on a less dense glass medium of
refractive index n2 = 1.430. Suppose that the free space wavelength of the light ray is 850nm
(a) What should be the minimum incidence angle for TIR?
(b) What is the penetration depth of the evanescent wave into medium 2 when i = 85 and when
i = 90?
(c) What is the reflection coefficient and reflectance at normal incidence (i = 0) when the light
beam traveling in the silica medium (n = 1.455) is incident on a silica/air interface?
(d) What is the reflection coefficient and reflectance at normal incidence when a light beam
traveling in air is incident on an air/silica (n = 1.455) interface? How do these compare with part
c and what is your conclusion?
3. TIR and polarization at water-air interface
(a) Given that the refractive index of water is about 1.33, what is the polarization angle for light
traveling in air and reflected from the surface of the water?
(b) Consider a diver in sea pointing a flash light towards the surface of the water. What is the
critical angle for the light beam to be reflected from the water surface?
4. Goos-Haenchen phase shift: A ray of light which is traveling in a glass medium of refractive
index n1 = 1.460 becomes incident on a less dense glass medium of refractive index n2 = 1.430.
Suppose that the free space wavelength of the light ray is 850nm. The angle of incidence i =
85. Estimate the lateral Goos-Haenchen shift in the reflected wave for the perpendicular field
component. Recalculate the Goos-Haenchen shift if the second medium has n2 = 1 (air). What is
your conclusion?
5. Bragg Diffraction Suppose that parallel grooves are etched on the surface of a
semiconductor to act as a reflection grating and that the periodicity (separation) of the grooves is
1 micron. If light of wavelength 1.3 m is incident at an angle 89 to the normal, find the
diffraction beams.