Homework Assignment 10 (due Sunday 4/26)

PHYS112 : Homework Assignments

Homework Assignment 10 (due Sunday 4/26)

Electromagnetic Waves and Geometric Optics

Goals :

Describe the intensity of electromagnetic waves emitted by an isotropic source as a function of distance

$\begin{displaymath} I = \frac{P_s}{4 \pi r^2} \end{displaymath}$
Relate the intensity of an electromagnetic wave, the amplitudes of its electric and magnetic fields, and the speed of light

$\begin{displaymath} I = \frac{1}{c\mu_o} (E^\mathrm{rms})^2 = \frac{c}{\mu_o} (B^\mathrm{rms})^2 \hspace{1.5cm} \frac{E}{B} = c \end{displaymath}$

$\begin{displaymath} E^\mathrm{rms} = \frac{E^\mathrm{max}}{\sqrt{2}} \hspace{3cm} B^\mathrm{rms} = \frac{B^\mathrm{max}}{\sqrt{2}} \end{displaymath}$

and use the Poynting vector (and the right hand rule) to relate the direction of propagation of an electromagnetic wave to the orientations of its electric and magnetic fields

$\begin{displaymath} \vec{S} = \frac{1}{\mu_o} \vec{E} \times \vec{B} \end{displaymath}$
Calculate the intensity of polarized light transmitted through a polarizing filter with Malus' law

$\begin{displaymath} I = I_o \cos^2 \theta \end{displaymath}$

( for unpolarized incident light.)
Relate the angle of incidence to the angle of reflection of an electromagnetic wave crossing a boundary between two materials using Snell's law

$\begin{displaymath} n_2 \sin \theta_2 = n_1 \sin \theta_1 \end{displaymath}$

and calculate the critical angle -the threshold for total internal reflection from a boundary between two materials

$\begin{displaymath} \theta_c = \sin^{-1} \frac{n_2}{n_1} \end{displaymath}$
Calculate the angle of reflection corresponding to maximum polarization via Brewster's law

$\begin{displaymath} \theta_B = \tan^{-1} \frac{n_2}{n_1} \end{displaymath}$
Draw ray diagrams and distinguish between real, virtual, inverted and upright images.
Relate the image and object distances of thin lenses and spherical mirrors

$\begin{displaymath} \frac{1}{o} + \frac{1}{i} = \frac{1}{f} \end{displaymath}$
Calculate the lateral magnification of a lens or mirror

$\begin{displaymath} m = -\frac{i}{o} = \frac{h'}{h} \end{displaymath}$

or a series of lenses and/or mirrors .
Calculate the angular magnification of an optical instrument

$\begin{displaymath} m_\theta = \frac{\theta'}{\theta} \end{displaymath}$
Apply the above concepts to optical instruments with multiple mirrors/lenses.

Your assignment is posted on the UT Homework Service (Class no. 99940)

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