**Problem 1:**

A spherical, shiny holiday decoration ball is acting as a convex mirror. The sphere has a radius of 4 cm. Your eye is 10 cm from the mirror. How much bigger or smaller is the image of your eye than the actual size of your eye? Is the image real or virtual, upright or inverted?

**Problem 2:**

For a symmetrical prism (one in which the apex
angle lies at the top of an isosceles triangle), the total deviation angle
ϕ of a light ray is minimized when the ray
inside the prism travels parallel to the prism’s base.

Assume that a beam of light passes through a glass
equilateral prism with refractive index 1.5. The prism is in air and is mounted
on a rotation stage, as shown in the figure. When the prism is rotated, the
angle by which the beam
is deviated changes. What is the minimum angle ϕ bywhich the beam is deflected?

**Problem 3:**

The region 0 ≤ z ≤ z_{0} is filled with a dielectric material of
permittivity ε = 4ε_{0 }and
permeability μ = μ_{0}.
A
linearly polarized wave of amplitude **E **= E_{0}**i
**and
angular frequency ω is incident normally on the interface at z = 0
from the region z < 0. Show that the ratio of the reflected intensity to the
incident intensity in the z < 0 region is

[1 + (16/9)csc^{2}(2ωz_{0}/c)]^{-1}.

**Problem 4:**

An electromagnetic wave with circular frequency ω propagates in a medium of
dielectric constant ε, magnetic permeability μ, and conductivity σ.

(a) Show that there is a plane wave solution in which
the amplitude of the **E** and **B** fields decreases exponentially along
the direction of propagation, and find the characteristic decay length.

(b) Simplify by
assuming that σ is great enough so that σ/(εω)
>> 1.

**Problem 5:**

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.