Science Buddies: "Ask an Expert"

I have posted this question some time ago but it was only upon registration, and that it only allows up to 500 characters in Project Questions. This time, here's the complete one:

The following questions are about an experiment where laser pointer can be used to determine the d (data track spacing) of CDs:


1. Is it possible to have a negative angle for θi ? If so, when does this happen?

2. What if the reflected ray isn't equal to θi ? Shall the reflected ray be ordered m=1 automatically ??

3. θi is placed to the right of the normal and there is a diffracted ray to the right of θi. What should this diffracted ray's order be ?? And the angle... is it positive or negative ??

4. What if the computed d is negative ?? Is this reasonable or absurd ?? Or is there something wrong with substitution of values, especially the signs ??

5. What if the averaged d-values for some order of diffraction column is negative ?? Is this an error ?? What does this mean ?

6. Since it is mentioned that the d computed using the formula d=mλ/(sinθm-sinθi) is in nm when λ is in nm, how is the computed value used in determining data track spacing ?? Is it that when d is large, then the CD has low storage capacity or the other way around ??
How shall the computed d-values determine storage capacity of CD ??

7. In my thesis' Review of Related Literature, there's a part that says, "On a CD, the space between tracks is about 1.6 microns versus spacing on a DVD-R which is about 0.74-0.8 microns."
If so, how can nm be converted to microns ? Is it possible ?

8. Can nm be converted to MB to see if the storage capacity label of a CD matches with the computed ones ? If so, how ?

9. Lastly, how is the d=mλ/(sinθm-sinθi) formula derived ?? What is the relationship of each variable to each other ?? What are the principles supporting this formula ??

Much help shall be appreciated. My paper is due on September 20, 2011 and the defending for my project is on Sept. 21, 2011 yet I am uncertain with what I am doing to the experiment. For your reply kindly do so in my email address which I entered upon registration.

1 ) The angles are measured from the normal to the reflecting surface (That's vertical in the illustrations). The formula given in the project discussion assumes that the diffracted beam is on the opposite side of the normal, and both angles are measured from the normal as positive values. If the incident and diffracted beams are on the same side of the normal, then one of them will be positive and the other one negative.
2 ) When the incident and diffracted angles are zero, then both sines are zero and the diffraction is zeroth order. As the angles move away from zero, then a delay occurs between the diffraction from one disc groove and its neighbors. The formula given is called The Grating Equation. If you do a web search for that title, you'll find several discussions for how it is derived and how to use it. Example: http://www.physics.smu.edu/~scalise/emm ... n/lab.html.
3 )Diffracted orders can appear in a variety of locations depending on the incident angle. You will see multiple orders, and you can check what order each one is after you get a value for d and require that m be an integer multiple for each one you see.
4 ) and 5 ) d must be a positive value. If you get a negative value, you must have the sign of an angle reversed.
6 ) If the tracks are close together or relatively far apart, how does that affect the number of tracks that can fit on the disk? How is storage capacity related to number of tracks?
7 ) Nanometers (nm) and microns are just two different units of measure. Look up how they relate.
8 ) Think about it given the other answers here.
9 ) See answer to 2)
Sorry this is late, but hope it helps.