| Topic: |
Science > Physics |
| User: |
"Dobri Karagorgov" |
| Date: |
28 Feb 2005 05:17:17 AM |
| Object: |
Levers In Support Of Lenses |
Lensing was concluded only experimentally, without theoretical
support. Here is how levers contribute in theoretical support of
lensing:
\begin{equation}\label{Archimedes' lever}
|W_1||D_1|=|W_2||D_2|
\end{equation}
Starting from \ref{Archimedes' lever} we get:
\begin{equation}\label{Lensing}
\left\lbrace\begin{array}{l}
\frac{1}{|W_1|}+\frac{1}{|W_2|}=\frac{1}{|W_f|}\\
\frac{1}{|D_1|}+\frac{1}{|D_2|}=\frac{1}{|D_f|}\\
\frac{|W_f|}{|D_f|}=\frac{|W_1|}{|D_2|}=\frac{|W_2|}{|D_1|}
\end{array}\right.
\end{equation}
this way:
$$1+\frac{|W_1|}{|W_2|}=\frac{|D_2|}{|D_1|}+1$$
$$\frac{|W_1|+|W_2|}{|D_1|+|D_2|}=\frac{|W_1|}{|D_2|}=\frac{|W_2|}{|D_1|}$$
$$\frac{|W_1|+|W_2|}{|D_1|+|D_2|}\frac{|W_1|+|W_2|}{|D_1|+|D_2|}=\frac{|W_1||W_2|}{|D_1||D_2|}$$
$$\lambda\frac{|W_1|+|W_2|}{|D_1|+|D_2|}=\frac{|W_1||W_2|}{|D_1|D_2|}$$
$$\lambda(\frac{1}{|W_1|}+\frac{1}{|W_2|})=\frac{1}{|D_1|}+\frac{1}{|D_2|}$$
The lever with focal weight $W_f$ makes us percieve the original
weight $W_1$ as an image weight $W_2$ (similarily for the distances).
"Unified Psycho Physics"
www.geocities.com/dedaNoe
section: "Levers as Lenses"
.
|
|
| User: "Dobri Karagorgov" |
|
| Title: Re: Levers In Support Of Lenses |
18 Mar 2005 09:16:31 AM |
|
|
all those equations were probably to confusing for you.
take a look at this figure you'll get the point:
www.geocities.com/dedanoe/lenses.gif
.
|
|
|
|
|
Related Articles |
|
|
