The Table unformated after I submitted it, I will try to add an image snapshot o

Question

The Table unformated after I submitted it, I will try to add an image snapshot of it, I hope it helps.

No need to do any of this just adding it to the information just in case it might help. The assignment was:

Fendt, W. (1997). Refraction of light (simulation). Retrieved on March 1, 2008, from http://www.walter-fendt.de/ph14e/refraction.htm

The first part of the simulation is a series of measurements designed to demonstrate the validity of Snell's Law. The light ray passes from medium 1, which has an index of refraction n1, into medium 2, with an index of refraction of n2. The angle of incidence is ?1, the angle of refraction ?2. Complete the table below. (The first line has been completed for you.) Explain in detail how your results demonstrate the validity of Snell's Law.

Then came the Table above with alot of the blanks empty I filled them from the simulation, however the empty blanks above are the ones I got wrong, hoping to get help fixing that.

This is the reply after I submitted the assignment:

Let's look at the first three cases.
I've deleted columns 1 and 3, and changed (theta) to a.
It's true that n1sin(a1) is approximately equal to n2sin(a2) in all cases, which validates Snell's law, but the values are NOT all 0.50.

Let's look at the second case:
n1sin(a1)=1*sin(59.9) =1* (0.87)=0.87
n2sin(a2)=1.46*sin(36.3)=1.46*(0.59)=0.86

I think you were expecting a degree of "symmetry" that wasn't there.

n1 n2 target a1 actual a1 n1sin(a1) a2 n2sin(a2)
1 1.46 30 30.3 0.500 20.2 0.500
1 1.46 60 59.9 0.865 36.3 0.864
1 1.46 90 90 1.000 43.2 0.999

I changed the (theta) to a. In the first table in this question as well so there was no confusion.

My detail description I submitted was not commented on, however if you would like to help on that I would appreciate it, not needed to be rated a Lifesaver though.

The best description I could find that explained Snell’s law best to my understanding of it came from http://en.wikipedia.org/wiki/Snell's_law :

Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the opposite ratio of the indices of refraction:
(Formual did not copy and paste)
with each ? as the angle measured from the normal, v as the velocity of light in the respective medium (SI units are meters per second, or m/s) and n as the refractive index (which is unit less) of the respective medium (Wikipedia, 2011).

The simulation showed the greater the difference in refractive index between the two media, the greater the difference was between angles of incident and the refracted angles, as well as the greater the refracted angles bent towards the norm. The opposite proved true as well, the closer the refractive index of the two media, the closer the angles of incident and refracted angles are, and the lesser change towards norm of the refracted angles.

Explanation / Answer

The values in the empty columns are calculated from the data in the other columns For example, in row 1, n1=1.00, a1=30.3, n2=1.46 a2=20.2 So the values for n1 sin a1 and n2 sin a2 can be calculated as follows: n1sin a1= 1.00 * sin (30.3) = .505 n2sin a2= 1.46 * sin (20.2) = .504 For the next row, the procedure is the same... n1=1.00, a1=60.3, n2=1.46 a2=36.5 n1sin a1= 1.00 * sin (60.3) = .869 n2sin a2= 1.46 * sin (39.5) = .469 Here are the remainder of all n1sin a1 and n2sin a2 values Row n1sin a1 n2sin a2 3 1.00 .999 4 .502 .502 5 .868 .868 6 1.00 1.00 7 .500 .499 8 .868 .867 9 1.00 1.00 10 .760 .762 11 1.32 1.32 12 1.52 1.52 This table of values shows that for for various mediums and indexes of refraction, n1(sin(a1)=n2(sin(a2)

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