Recent content by derek e

I think it can be useful to consider a medium with a "larger" index of refraction as a "thicker" string and a medium with a "smaller" index of refraction as a "thinner" string, then visualize the physics of a wave propagating down the two strings tied together, end-on-end.

Here's what I do: I have a desktop that runs Vista. On it, I have http://www.virtualbox.org/" and a virtual Ubuntu machine that is my Linux workhorse. I also have some kernels that I can dissect. For portability, I have a net-book with a copy of Ubuntu on it. The net-book was $300 and does...

It's probably best to split our peas and carrots. The method of Lagrange multipliers does not reduce the number of variables or the number of equations. What it does is incorporate the constraint information by adding a term to the constrained equation, then it observes a parallel gradient...

I was kinda playing. But what I think is more subtle is the use of the words "wrong" and "incorrect." If one were trying to make a definition of something containing the essence of an idea, such as curvature, then I could see how some definitions can be considered wrong or incorrect. Something...

I guess the gist of it is that when you eliminate variables using constraint equations, you are incorporating information about your system into the problem. When extremizing the result, the information is utilized, consequently, during differentiation. i.e. You no longer regard certain...

... unless a useless definition is defined to be something that is incorrect or wrong. :tongue:

Like others said, this is by definition. You might be interested in the http://en.wikipedia.org/wiki/Gamma_function" .

I think you need to slow down, reread what we have written, reread the problem statement and carefully think through it.

You can check out Introduction To Modern Optics by Fowles for a classical mathematical description of the phenomenon. This book casts Huygen's principle into the Fresnel-Kirchhoff Formula and then applies it in several settings. If you think about it, shrinking the aperture localizes the...

Let 2y = sinh(a). Let \alpha=sinh^{-1}(0) and \beta=sinh^{-1}(2). Then \begin{equation*}\begin{split} \int_0^1 \sqrt{1 + (2y)^2}dy &= \frac{1}{2}\int_\alpha^\beta cosh^2(a)da \\ &= \frac{1}{2}\int_\alpha^\beta \frac{1 + cosh(2a)}{2} da \\ &= \frac{1}{4}\left[a +...

Hi, interesting question. I don't know the answer but I googled some pictures of WWI planes. A lot of them had two layers of wings that look like they have some curvature. This combined shape looks like a silhouette of sections of an airfoil, (from Cyrus) probably because each wing is an...

edit: Use If a < b, then c * b < c * a if and only if c < 0. Spoiler : We have x < 0, y < 0 and x < y. Then x * y < x * x, because x < 0. Similarly, y * y < y * x, because y < 0. So, y^2 = y * y < y * x = x * y < x * x = x^2, giving y^2 < x^2. o:)

As far as I can tell, the main benefit of being a physicist is physics. You should think about what is important to you and find a way to factor it into the equation. Personally, I plan on continuing my formal physics education later in life. This isn't standard, but that's not how I roll :biggrin:

I don't think you will get very far since V=iR. Taking the rms (root-mean-square) of a value means you perform the operations in the name in reverse order. So, you take a value, square it, find the mean of the squared value and then take the square root of the result. The final value is the rms.

The gist of how one way mirrors work is that a piece of glass is coated with less silver than a regular mirror. This allows more light to be transmitted through the mirror. Light is still reflected, however, and, between a light and dark room, an observer in a lighted room will see an abundance...