tush

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Problem Solving Strategies

General chat for high school physics. For MathJax see meta.sta...

tush

Jan 30 14:54

tush

Jan 30 14:54

- dA cosθ is the projected area of dA on the observer

- cos α is the projection of the line of sight of the observer on the line connecting dA to the observer

Do you agree?

tush

Jan 30 14:54

tush

Jan 30 14:53

What is the solid angle subtended by the infinitesimal element of area dA as seen by an observer whose eyesight is indicated by the blue vector?

The distance between the observer and and the element of area is dA.

I think that the answer is

tush

Dec 3, 2024 09:35

@JohnRennie Problem solved. Integral was evaluated for the wrong limits. Thanks anyway!

tush

Dec 3, 2024 08:52

Ok. ping me and I will show up

Thanks very much!

tush

Dec 3, 2024 08:49

Hi :)

tush

Dec 3, 2024 08:49

@tush question about solid angle

tush

Dec 3, 2024 08:49

@JohnRennie Do you mind taking a look at this question?

tush

Dec 1, 2024 13:54

tush

Dec 1, 2024 13:54

@tush Set up is as in the picture below:

tush

Dec 1, 2024 13:35

Integrating this expression for dΩ from θ=-pi/2 to +pi/2, I get zero.
I simply can't find the error in my approach. Any help? Can anyone tell me what I am missing?

tush

Dec 1, 2024 13:33

tush

Dec 1, 2024 13:31

tush

Dec 1, 2024 13:31

tush

Dec 1, 2024 13:29

tush

Dec 1, 2024 13:29

tush

Dec 1, 2024 13:28

tush

Dec 1, 2024 13:27

This way:

tush

Dec 1, 2024 13:27

and then to integrate over theta from -pi/2 to +pi/2, and phi from 0 to 2pi.

tush

Dec 1, 2024 13:25

tush

Dec 1, 2024 13:25

To do that, I am trying to find the solid angle subtended by dA, an infinitesimal surface element on the sphere, by taking into account the projection of \hat{n} (unit direction normal of dA) on the line connecting the observer to dA:

tush

Dec 1, 2024 13:25

tush

Dec 1, 2024 13:24

I want to find the solid angle subtended by the half sphere of radius R, with its center at the origin, as seen by an observer standing at (0,0,Z), as in the attached picture.

tush

Nov 23, 2024 07:09

Hmm.. Okay

tush

Nov 23, 2024 07:06

@JohnRennie I integrated over theta and the solution to the integral involves the log I mentiond.

tush

Nov 23, 2024 06:49

A solution to a physics problem I am working on involves an integral of some expression of angle theta, radius R and distance Z.
Evaluating the definite integral over theta in Wolfram, one of the terms I get is log[(R-z)^2]. If I remember correctly from my bachelor studies, arguments for functions like log, exp and sine must be unitless. I.e. (R-z)^2 has the units of distance squared.
Do you think I am going wrong here because of the dimensions inside the log?

tush

Jul 24, 2024 10:44

Then I will ask in digital signal process.

tush

Jul 24, 2024 10:43

tush

Jul 24, 2024 10:43

I am talking about a stationary signal, as in here:

tush

Jul 24, 2024 10:43

The thing is that this signal has zero amplitude for large t.

tush

Jul 24, 2024 10:42

tush

Jul 24, 2024 10:42

@JohnRennie Its FT is

tush

Jul 24, 2024 10:39

@JohnRennie Signal processing perhaps?

tush

Jul 24, 2024 10:38

@JohnRennie At least, can you tell me which SE website fits this question? Do you think that the physics.SE is the right place?

tush

Jul 24, 2024 10:37

The auto-correlation is something that we learn in optics courses in the context of cohrence

tush

Jul 24, 2024 10:36

@JohnRennie Really? That's a basic undergraduates topic

tush

Jul 24, 2024 10:35

Note that I am talking about a stationary signal, as emphasized in the figure below, taken from Saleh and Teich Photonics textbook

tush

Jul 24, 2024 10:34

tush

Jul 24, 2024 10:34

I want to find the auto–correlation of a broadband stationary signal.

The frequency spectrum of the signal is centered around ν₀ and had width Δν, as in the figure below

tush

Jul 24, 2024 10:24

@JohnRennie Hello
Are you available for a question?

$Mathematics$ Mathematics

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tush

Nov 28, 2024 11:41

@tush I think that my question is superfluous. 1/(z+1) is already written as a power series in the above mentioned domain. I.e. there is no need to manipulate it any one way or another.

tush

Nov 28, 2024 11:37

@SineoftheTime Any numerical value or a polynom of z that I am having trouble finding, and that satisfies the equation.

tush

Nov 28, 2024 11:34

and then to use the familiar geometric series?

tush

Nov 28, 2024 11:34

tush

Nov 28, 2024 11:34

I need to find the Laurent series for the function 1/(z+1) in the domain |z+1|<1.
Do I need to write the function as

$TeX - LaTeX$ TeX, LaTeX and Friends

\begin{chat}

tush

Sep 29, 2024 18:24

Thanks. I once read a few chapters from this book. Perhaps I should read again it more carefully again.
Either way I would like to understand the math in the perspective library I.

tush

Sep 29, 2024 17:49

TikZ has a library called "perspective" that renders 3D scenes to the 2d canvas in perspective (so that objects far away from the viewer appear smaller).
I am interested in understanding the geometrical calculations behind perspective drawings, and I want to implement this projection in another programming language.

So I looked at the library's code, which is not long, but because I don't have any knowledge in core-pgf macros, I have a few missing links. I am not sure what the library does to the x, y and z coordinates of the point I am plotting in it.

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tush

Jul 22, 2024 14:03

tush

Jul 22, 2024 14:01

Is there a built-in function to perform the cross correlation of two functions? There is Convolve[f,g,x,y] which is similar but not identical.