PES 2130: Homework assignment 7 [24 points]

Handed out: Monday October 20Due in: Monday October 27, at the start of class

Show all working and reasoning to receive full points.

Part 1: fully graded questions [18 points]

Question 1 [5 points]A linearly polarized electromagnetic wave travels in the negative x-directionand strikes a perfect conductor (zero resistivity) that is placed in the yz-plane. The currents induced in the conductor produce a reflected wave thattravels out from the plane in the positive x-direction. The superpositionprinciple states that the total electromagnetic wave is the vector sum of theincident and reflected electromagnetic wave. The E-field and B-field of thistotal (standing) electromagnetic wave are~E(x, t) = −2Emaxsin(kx)sin(ωt)j,~B(x, t) = −2Bmaxcos(kx)cos(ωt)k.a)[2.5 points] Using these wave functions find the Poynting vector. Use2sin(A)cos(A)=sin(2A) to simplify your result.b)[1.5 points] Calculate the intensity of this electromagnetic wave.c)[1 point] Given your result in part b), what does an engineer have to con-sider when using electromagnetic waves to transmit power?

Question 2 [6 points]A certain type of glass has an index of refraction of 1.650 for blue light ofwavelength 430 nm and an index of 1.615 for red light of wavelength 680 nm.If a beam containing these two colors is incident at an angle of 30o on a 30.0cm thick slab of glass, how far apart are the red and blue rays when theyemerge from the glass? For full points you need to draw a diagram.

Question 3 [4 points]An observer sees a mirage ahead on a perfectly straight road. This occurswhen air immediately above the pavement gets hot and has a different re-fractive index compared to normal air. Assume that the observer’s eyes are1.7000 m above the road (or layer of hot air). If the index of refraction ofnormal air is 1.0029 and the observer sees the mirage 100.00 m ahead, whatis the index of refraction of the hot air? To solve this problem, assume thattotal internal reflection is taking place. For full points you need to draw adiagram.

Question 4 [3 points]A polarized light beam passes through a polarizing filter. The intensity of thelight passing through the filter is I, when the angle between the polarizingaxis of the filter and the direction of polarization of the light is θ. Now youwant the intensity to be I/2. To achieve this, what is the angle between thepolarizing angle of the filter and the original direction of polarization of thelight? Your final answer should be in terms of θ.

Part 2: completion grade only [6 points]

In this section you must fully complete 3 problems from the textbook to score6 points in total. If you do everything correct in a problem, you will get 2points for it. If you get something wrong but make a reasonable attempt,you will get 1 point for a problem. No attempt or an unconvincing attemptwill score zero.

To get the full 2 points you must:

• Write down all known and unknown variables clearly

• Draw a diagram

• Include all mathematical and logical steps, including assumptions

• Get the correct answer with the correct units and significant figures

Please grade this section yourself using the answers at the back of the book.The grader will check that you have not cheated by awarding yourself toomany points.

This week’s questions are:

• Chapter 33, Problem 15 [2 points]

• Chapter 33, Problem 33 [2 points]

• Chapter 33, Problem 65 [2 points]

Book problems