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299 HW10 (Questions 54 – 56)
Worked solutions due in Lecture on 12/05/
NAME____________________________________________________________
(please print)
Grading Option: Syllabus Alternative (Circle one, default syllabus)
- Consider a 3 dimensional linear polarized Electromagnetic wave with the Electric field polarization along
the y axis and whose Electric and Magnetic fields are given by the following expressions:
E r , t =
E
0
cos
k ⋅ r − t y
B r , t =
B
0
^5
cos
k ⋅ r − t x
where (^) r = x x y y z z and
k = k x
x k y
y k z
z. The three dimensional wave equation for a wave
function x , t is given by
c
2
2
x , t
∂ t
2
2
x ,t
Show that both E and B satisfy this equation. Compute the Poynting Vector and along which direction does
Electromagnetic energy from these fields flow? (5 points)
- Consider an initially unpolarized point light source of power 300 Watts. Suppose that this source is 10
meters away from a small polarizer. Approximating the the polarizer initially as a point. Find the
intensity of the light on it. Now, Suppose that the polarizer polarizes the light at an angle of 25 degrees
with respect to the horizontal. The remaining light is incident on a second polarizer very close to the first
one. This one polarizes at an angle of -30 degrees. The remaining light hits a third polarizer which
polarizes at an angle of 15 degrees. Compute the intensities of light incident on all of the polarizers and
the intensity of light that exits the polarizer system. (See homework 10 problem 57 for a graphic.) (
points)
BONUS (10 points)
Consider the following spherical mirror with the optical axis given by the dotted line.
(i) Clearly label the points of interest for this mirror. (1 point)
(ii) If the f=10cm and the object is at a distance of 5cm. Compute the location of the image. Draw it on the
diagram above. (1 point)
(iii) Is the image real or virtual? (1 point)
(iv) Is it magnified or diminished, upright or inverted. What is the magnification of the image?
(v) Repeat parts (i)-(iv) for a symmetric diverging lens. Draw the diagram yourself. (5 points)
