Assignment 3, solutions

Problem 1:

imageA 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 δmin.
(b)  Give a numerical value for δmin if A = 60o and n = 1.5.

Solution:

Problem 2:

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.

Solution:

Problem 3:

(a)  Write down Maxwell's equations for a conducting medium with conductivity σ, permittivity ε0 and permeability μ0,
(b)  A plane wave of low frequency ω << σ/ε0 is propagating in the z-direction inside the conducting medium.
Let E = E0exp(i(kz - ωt)),  B = B0exp(i(kz - ωt)), where E0, B0, and k are complex.
Use Maxwell's equations to show that k = k1 + ik2, k1 ≈ k2 ≈ (μ0ωσ/2)½.
Calculate the ratio of the complex amplitude of the two fields, E0/B0 (magnitude and phase).
(c)  Calculate the energy flux (time averaged Poynting vector) in the conducting medium.

Solution:

Problem 4:

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.

Solution:

Problem 5:

imageLight 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.

Solution: