Need some pointers on some puzzling questions

[Watsonb2]

Hey all,

I'm taking a physics class dealing with harmonic motion and wave motion, and the last homework assignment of the quarter was given a bit late (i.e. after we began to cover extraneous lectures that are abstract and challenging), so I'm finding it hard to get back into the swing of things for the following problems. *Unfortunately, I'm away from both my book and the prof. so I don't have the luxury of consulting either for help at the moment...

As per the spirit of the forum, I'm not looking for answers, merely pointers on what I should go back and look over in order to get started...

Homework Statement

1) Malus' Law, insofar as it pertains to systems of two or three polarizers. The prof went over this in class, but I can't seem to find the necessary formula to deal with problem that he's given. Does anyone know how this theorem applies when a vertical polarizer and a second of 60 degrees and a third of 45 degrees is placed into a light's path?

2) The next question deals with linear polarization and our having to determine the equation for the electric and magnetic fields in a vacuum. For the life of me, I can't see how I'm supposed to start as I only remember him talking about actual polarizers, not their respective graphs in the 3D plane. The question specifically asks me about the radiation being polarized in the y-z plane at either 0 or 45 degrees. Any thoughts on the formula I should use to solve this problem?

3) In dealing with a Double Slit Interference apparatus, how do I "design" it so that the central diffraction peak contains 17 fringes? For the problem, I have to assume that the first diffraction minimum occurs at; first, an interference minimum, and second and interference maximum. These problems gave me trouble at the best of times so any help you can offer would be great...

Homework Equations

*See above

The Attempt at a Solution

1) The basis for Malus' Law is: Polarized Intensity = Initial Intensity x Cos^2(The angular deviation from the incident angle).

Do I simply substitute the angles I'm given if I need to find the intensity of the transmitted light, I, in terms of the initially unpolarized light (Io)?

2) This one has me stumped as I don't even know where I should begin equation-wise, unless I simply look at the trigonometric curves that already define the E and B fields in the 3D plane...

3) I'm assuming that for this one, I definitely need to think of my m as being 17, to make sure I include all of the interference fringes. Since I need both a minimum and a maximum, do I also need to consider both: m(wavelength) and (m+1/2)(wavelength) as per the definition for an interference min and max?

Hope you all can provide a bit of insight, as all of this new information is a bit overwhelming when you're first introduced to it...

Thanks,

B

 

[Redbelly98]

(1) For Malus's Law, the transmission of each polarizer is cos²θ as you said. θ is the angle between the polarizer orientation and the incident polarization. So for the 2nd, 3rd, etc. polarizers, θ is the angle between that polarizer and the previous one.

(2) I don't understand what, specifically, you are asking here.

(3) The central diffraction peak width is given by the single slit diffraction formula, using the width of either slit. For the interference fringe spacing, use the double slit diffraction formula.

Also, m is not simply 17. It is 0 for the central fringe, some value m_max at one edge of the central peak, and -m_max at the other edge.

 

[Watsonb2]

Thanks for the insight on the 1st and 3rd questions mate, confirmed what my thoughts were (and changed them in the 3rd one)...

As far as the second question goes, there wasn't a good way to phrase it without just writing down the actual problem...and I wasn't sure how that would be taken. I am, however, still stumped as to what I need to do, so maybe I'll go ahead and post the question:

"Write down the electric field and associated magnetic field in a vacuum for traveling plane waves for the following cases.

a) The radiation is linearly polarized in the y-z plane at an angle of 0 with the y axis, and is traveling in the +x direction.
b) The radiation is linearly polarized in the y-z plane at the angle of 45 degrees with the y-axis and is traveling in the +x direction."

When I look it over again, it seems like it might have a REALLY simple answer, but for the life of me, I just don't think that's what I need to do...

Any thoughts are appreciated...

-B

 

[Redbelly98]

Okay, thanks for clarifying that. Ummm, are there any examples in your textbook where they write the E-field for a traveling plane wave? (Hopefully you have access to your book by now, you didn't yesterday.)

One hint: the equation would use unit vectors to indicate the direction of E (i.e. the polarization).

I'm logging off for the night (Eastern USA time zone, nearly midnight), so good luck and I'll be back online tomorrow if you're still stumped.