|
GR0177 #97
|
|
|
Problem
|
|
|
This problem is still being typed. |
Optics }Refraction
From Snell's Law, one obtains  \sin\theta^{'}) , since the index of refraction of air is about 1.
Now, differentiate both sides with respect to  .
 \sin\theta^{'})\\
0&=& \frac{dn(\lambda)}{d\lambda} \sin\theta^{'}+(n(\lambda) \cos\theta^{'}) \frac{d\theta^{'}}{d\lambda}\\
\delta \theta^{'} &=& |\tan\theta^{'}/n \frac{dn(\lambda)}{d\lambda} \delta \lambda|, <br />
\end{eqnarray})
which gives choice (E) to be the angular spread.
This solution is due to ShyamSunder Regunathan.
|
|
|
Alternate Solutions |
jsdillon
2008-04-07 20:27:09 | This problem can be solved using the limiting case of  =0.
We also know that  ' must go to 0 at =0 since normally incident rays don't refract (think Snell's Law with =0). That leaves only (E), the correct answer. (D) doesn't work because as goes to 0, ' also goes to 0.
(I thought, since I'm now almost all the way through all four tests with the exam now 6 days away, that I'd leave a small contribution. Thanks Yosun!) |  |
|
|
Comments |
barson
2009-10-18 04:39:38 | How to define the theta which depends on lamda?
I got some confuse about this. |  | realcomfy
2008-10-24 14:16:00 | Just curious, but how does the ) turn into just plain  in that final solution?
nobel
2008-11-01 07:34:16 |
n(lambda) implies n is a function of lambda. its not
n *lambda
|
|  | jsdillon
2008-04-07 20:27:09 | This problem can be solved using the limiting case of =0.
We also know that ' must go to 0 at =0 since normally incident rays don't refract (think Snell's Law with =0). That leaves only (E), the correct answer. (D) doesn't work because as goes to 0, ' also goes to 0.
(I thought, since I'm now almost all the way through all four tests with the exam now 6 days away, that I'd leave a small contribution. Thanks Yosun!)
Daw6
2009-11-05 10:43:05 |
We can also think about the limiting case n()=1, i.e. no change in medium is taking place. In this case,  '= 0 also. The only two choices that provide this contain a factor of dn/d, and only (E) provides the aforementioned limiting case as well.
Just a thought.
|
apr2010
2010-04-09 16:56:08 |
Following your argumentation, D is possible.
I would just say, as Snells law contains also  choose D over E.
|
| | Mexicana
2007-10-02 18:23:52 | Another funky way of doing this (somehow less abstractly than yosun) is to use the general formula for combination of errors which would give for this case ^2=(\frac{\partial \theta'}{\partial\lambda})^2(\delta\lambda)^2) . Then you just need to get ^2) using Snell's Law. Whenever you see the word 'spread' or 'uncertainty' or just 'error', always remember the pretty formula for combination of errors!
Richard
2007-10-30 22:20:00 |
Personally, I find this to be more correct.
There seems to be a bit of hand-waving in dear Yosun's quoted solution. In particular, I am thinking of the last step.
|
| | scottopoly
2006-10-29 23:57:28 | Really minor, but the problem says it's in a vacuum, so your comment that it's in air is incorrect. |  |
|
| Post A Comment! |
|
|
Bare Basic LaTeX Rosetta Stone
|
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces  .
|
| type this... |
to get... |
| $\int_0^\infty$ |
 |
| $\partial$ |
|
| $\Rightarrow$ |
|
| $\ddot{x},\dot{x}$ |
 |
| $\sqrt{z}$ |
 |
| $\langle my \rangle$ |
 |
| $\left( abacadabra \right)_{me}$ |
_{me}) |
| $\vec{E}$ |
 |
| $\frac{a}{b}$ |
 |
|
|
|
|
|
