A laser beam enters a prism from air. For a symmetrical prism (one in which
the apex angle lies at the top of an isosceles triangle), the total deviation
angle δ of the beam is minimized when the light ray inside the prism travels
parallel to the prism's base.

(a) If the index of refraction of the glass is n and
the apex angle is A, find total deviation angle δ_{min}.

(b) Give a numerical value for δ_{min} if A = 60^{o} and
n = 1.5.

A beam of monochromatic light of wavelength λ in vacuum is incident normally on a nonmagnetic dielectric film of refractive index n and thickness d. Calculate the fraction of the incident energy that is reflected.

(a) Write down Maxwell's equations for a conducting medium with conductivity σ,
permittivity ε_{0} and permeability μ_{0},

(b) A plane wave of low frequency ω << σ/ε_{0} is propagating in the
z-direction inside the conducting medium.

Let **E** = **E**_{0}exp(i(kz - ωt)),
**B** = **B**_{0}exp(i(kz
- ωt)), where **E**_{0}, **B**_{0}, and k are complex.

Use Maxwell's equations to show that k = k_{1} + ik_{2}, k_{1}
≈ k_{2} ≈ (μ_{0}ωσ/2)^{½}.

Calculate the ratio of the complex amplitude of the two fields, E_{0}/B_{0}
(magnitude and phase).

(c) Calculate the energy flux (time averaged Poynting vector) in the
conducting medium.

In a double-slit experiment with 500 nm light, the slits each have a width of
0.1 mm.

(a) If the interference fringes are 5 mm apart on a screen which is 4 m from
the slits, determine the separation of the slits.

(b) What is the distance from the center of the pattern to the first diffraction
minimum on one side of the pattern?

(c) How many interference fringes will be seen within the central maximum in
the diffraction pattern? Draw a sketch of the pattern.

Light is incident along the normal on face AB of a glass prism of index of refraction 1.52, as shown in the figure.

Find the largest value the angle α can have such that there is no light
refracted out of the prism at face AC if

(a) the prism is immersed in air.

(b) the prism is immersed in water.