Recent content by dustydude

Homework Statement I trying to figure this out, its part of a bigger question. When ka \ll 1, what happens to, \frac{1}{\left ( 2-k^{2}a^{2} \right )\textup{sin}\, ka\, - 2\, ka \textup{cos}\, ka} Homework Equations Its something to do with the lowest order approximation. The...

Thanks for pointing that out Dick, minor error. (2,0,1) Its still not the right answer which is 1/271/2(5,1,1)

Find Unit Vector perpendicular to the Surface, x3+zx=1 at the point P=(1,2,-1) I figures that the perpendicular vector would be, N(X)=grad(x3+zx) = (3x2+z, 0, x) N(P)= (3,0,1) Then the unit vector would be, n=N(P)/||N(P)|| n=(3/51/2,0,1/51/2) The answer i get is not the...

Thanks for the comments ppl!

Thanks for the reply. If i understand what your getting at then the method in the links are used when fitting a curve to data points. The only measured value is y and I am looking for the error in x. a,b,c have one variable in common but also other variables. All the variables have an Error...

Hello, I'm looking to derive the error of a quadratic equation as a function of x. y=ax2+bx+c y is measured and variables a,b,c have an associated error Da,Db,Dc To solve for x you complete the square. x=&\pm\sqrt{\dfrac{y-c}{a}+\dfrac{b^{2}}{4a^{2}}}\mp\dfrac{b}{2a} If the variables y,c...

I see now i get what u mean by minimize. Find the value of d^2 which is the smallest. The smallest value of d^2 is 20. so d=2(5)^1/2

sorry i mean t=20

so t=5 is the time where the distance between the line is at a minimum? ...visualisation helps sometimes the substitue t into X(t) and then find distance betweeb X(t) and Q?

How can you minimize f(t)=20+4t2? Is it not only do when is a minus?

I've minimised d^2 by taking the derivative and setting to 0

Homework Statement There is points: P=(1,2,3,4) Q=(4,3,2,1) and line L passes through P and is parallel to A A=(1,1,1,1). X(t) is anypoint on line L. 1. Find the distance between X and Q as a function of t. 2. Find the minimum distance between Q and the line.(which is 2(51/2))Homework...

I like the idea of using a gas for collisional broadening. Any ideas on the type of gas? Maybe for a green Nd:yag(532nm) laser. Would anything be wrong have the beam pass through a coloumn, which contains the gas and controls the pressure. A concern would be that there are a lot of different...

There isn't anything is the wiki article about laser halfwidths. I'm talking about a laser with a few nm halfwidth.

Is it possible to widen the spectral FWHM of a laser beam. Any ideas? I understand the lasing process leads to the monochromaticity, but such a intense light source can have other uses. Thanks