Homework Assignments I - XV

PHYSICS 262

Spring, 2003 Daniel Finley

Homework Assignments I - XV , prior to the first Exam

There is a homework assignment due (almost) every class period!
If on paper, they should be turned in at the alphabetically-labeled box at the front of the classroom, before class begins!
If on WebAssign, they are due at 1 AM of the night of the day mentioned, which is of course actually very early in the morning of the next day.

No. I: due on viernes, 24 de enero

  1. 1 question and 2 problems, on paper, due at classtime:
    1. Chapter 17: Problems 3E and 9P,
    2. Chapter 34: Question 1

Solutions to HW 1 may be accessed after they are due, by clicking right here.

No. II: due on lunes, 27 de enero

  1. a paper problem, due at classtime, Monday:
    Begin with Eqs. (34-11) and (34-17), which result from applying the two Maxwell equations to our particular shape for an electromagnetic wave. Then show that the following equations are true, where we use Eq. (34-18) for the speed of light, c:

    Restricting to the case where the electric and magnetic fields depend only on time and the variable along the direction of propagation, these are the wave equations for these fields.

    As we know, the harmonic waves are acceptable solutions for these equations. However, now show that if f = f(w) is any, arbitrary function of one variable,
    then E = f(x±ct) and B = f(x±ct) are also solutions.

  2. 2 problems, from Chapter 34, on WebAssign:

Solutions to HW 2 may be accessed after they are due, by clicking right here.

No. III: due on miercoles, 29 de enero

  1. There are NO paper problems due today.
  2. 3 problems on WebAssign, 2 involving phasors from Chapter 17, and 1 from Chapter 34. [Note that the graph suggested at the end of the second problem is NOT required.]

Solutions to HW 3 may be accessed after they are due, by clicking right here.

No. IV: due viernes, 31 de enero

  1. There are no paper problems due today.
  2. 3 problems concerning polarization, on WebAssign, due tonight.
Complete solutions to HW 4 may be accessed after they are due by clicking right here.

Bonus Problem Number 1: worth 1 weeks' worth of homework points
due in 1 week [7 February]
[Scores added on top of final HW score at the end of the semester.]
A complete solution to this problem may be accessed after it is due by clicking right here.

No. V: due lunes, 3 de febrero

  1. A paper problem here. Please turn this one at the beginning of classtime, on Monday.
    How thick must a sheet of mica be if it is to form a quarter-wave plate for yellow light, of wavelength 589 nm? Mica cleaves so that the appropriate indices of refraction are 1.6049 and 1.6117.
  2. 4 relatively simple problems, from the last sections of Ch. 34, due on WebAssign, tonight.
Complete solutions to HW 5 may be accessed after they are due by clicking right here.

No. VI: due miercoles, 5 de febrero,

  1. There are no paper problems due today.
  2. 2 questions and 2 problems, on WebAssign, due tonight.
    However, notice that the first question is more of a "game" than an overly serious question; therefore, I have weighted it only 1/2 total point, for its 3 parts.
Complete solutions to HW 6 may be accessed after they are due by clicking right here.

No. VII: due viernes, 7 de febrero,

  1. There is one paper problem due today:
    Chapter 35.12P.
  2. 2 problems and 2 questions, on WebAssign, tonight.
    The first problem is quite long!
Complete solutions to HW 7 may be accessed after they are due by clicking right here.

No. VIII: due lunes, 10 de febrero,

  1. One Paper Problem: due at classtime on Monday:
    Consider the following question that could, for instance, be applied to your own eye. We want to generalize the lensmaker's equation given in the text to one where there are three indices of refraction involved: we have a lens, of index n, which separates one medium, with index n1, from another medium with index n2. The example of your eye is that the lens of your eye has "aqueous humor" on one side and "vitreous humor" on the other, fluids with index of refraction approximately 1.34. [Truthfully, their indices of refraction are not much different, but ... .] Another example is a lens being used to separate you from a large fish tank, set up so that you can see more of the tank than otherwise.

    The question I am asking you to answer is what would be the correct generalization of the lensmaker's equation for this case, with n1 on one side of the lens, n for the index of the thin lens itself, and n2 on the other side?

  2. WebAssign: Rather a long set, but fun, simple and interesting:
    3 questions and 2 problems from Chapter 35.
Complete solutions to HW 8 may be accessed after they are due by clicking right here.

No. IX: due miercoles, 12 de febrero,

  1. There are no paper problems due today.
  2. On WebAssign there are 4 problems from Chapter 35. The last one describes the human eye in a little detail.
Complete solutions to HW 9 may be accessed after they are due by clicking right here.

No. X: due viernes, 14 de febrero,

  1. One paper problem due at classtime today:
    The power P of a lens is defined as P = 1/f, where f is the focal length. The unit of power is the diopter, where 1 diopter = 1 m-1.
    1. Why is this a reasonable definition to use for lens power?
    2. Show that the net power of two lenses in contact is given by P = P1 + P2, where P1 and P2 are the powers of the two lenses.
    (Hint: See Problem 35.29P.)
  2. There are 2 WebAssign problems and 2 questions due tonight. The question is from Chapter 36, on two-wave interference.

Complete solutions to HW 10 may be accessed after they are due by clicking right here.

Bonus Problem Number 2: worth 1 week's worth of homework points (as usual).
due in 1 week [21 February]
The equation 1/p + 1/i = 2/r for spherical mirrors is an approximation that is valid if the image is formed by rays that make only small angles with the central axis. In reality, many of the angles are large, which smears out the image a little. You can use a computer to find out how much. Refer to Fig. 35-20 and consider a ray that leaves a point source (the object) on the central axis and that makes an angle with that axis.

First find the point of intersection of the ray with the mirror. If the coordinates of this point are x and y and the origin is placed at the center of curvature, then y = (x + p - r)tan and x2 + y2 = r2, where p is the object distance and r is the mirror's radius of curvature. Use tan = y/x to find the angle at the point of intersection, and then use + = 2 to find the value of . Finally use tan = y/(x + i - r) to find the image distance i.


Figure 35-20.

  1. Suppose r = 12 cm and p = 20 cm. For each of the following values of , find the position of the image, that is, the position of the point where the reflected ray crosses the central axis: 0.500, 0.100, 0.0100 rad. Compare the results with that obtained with the equation 1/p + 1/i = 2/r.
  2. Repeat the calculations for p = 4.00 cm.

A complete solution to this problem may be accessed after it is due by clicking right here.

No. XI: due lunes, 17 de febrero,

  1. There are no paper problems due today.
  2. There are 1 questions and 3 problems for WebAssign, all from Chapter 36, due tonight.

Complete solutions to HW 11 may be accessed after they are due by clicking right here.

No. XII: due miercoles, 19 de febrero,

  1. There are no paper problems due today!
  2. WebAssign: 5 questions and problems involving interference and diffraction are due tonight.
Complete solutions to HW 12 may be accessed after they are due by clicking right here.

No. XIII: due viernes, 21 de febrero,

  1. There are no paper problems due today!
  2. WebAssign: 4 problems involving interference and diffraction are due tonight.
Complete solutions to HW 13 may be accessed after they are due by clicking right here.

No. XIV: due lunes, 24 de febrero,

  1. One paper problem, due at classtime:
    Using the phasor analysis described in your text, create an equation for the intensity on a distant screen due to interference of light coming through two slits a distance d apart, but which are of different widths.
    Let the smaller slit have width a, and intensity exiting from it of amount I0, while the larger slit has width 4a. Then determine an equation for the total intensity of the light on the screen as a function of angle away from the central axis line, halfway between the two slits (as usual).
    Please make a graph of the relative intensity. How large are the maxima; at which angles do they appear? How small are the minima; at which angles do they appear?
  2. There are 3 WebAssign problems, concerning gratings.
Complete solutions to HW 14 may be accessed after they are due by clicking right here.

No. XV: due miercoles, 26 de febrero,

  1. There are no paper problems due today.
    DO download the equations sheet (from homepage) for the exam on Friday.
  2. There are 3 WebAssign problems due tonight; 2 on the Michelson interferometer, and one on relative speeds (Ch. 38).

Complete solutions to HW 15 may be accessed after they are due by clicking right here.

FIRST EXAM will be on Friday, 29 February.

Coverage will be Chapters 34-37, and also portions of 17, i.e., all of optics, and the waves that we have discussed.
A listing of equations for the exam, in Acrobat format, may be accessed here. You may bring these sheets with you to the exam itself, and write on the backs if you so desire.
Solutions may be accessed here.

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Last updated/modified: 21 February, 2003