- #1
wormhole
- 29
- 0
i'm trying to find a mirror shape which focuses a light at some specific point [itex]x_0[/itex]
the initial equation i derived for determining the shape of the mirror is:
(assuming that light rays fall parallel to x-axis - light source is very far from the mirror)
f(x) is the shape I'm trying to determine
[tex]
x_0=-\frac{f(x)-\tan(2\arctan(\frac{df}{dx}))x}{\tan(2\arctan(\frac{df}{dx}))}
[/tex]
basicly this is an expression for a line passing through point [itex]x_0[/itex] and point on
f(x) where light reflected.
so [itex]\tan(2\arctan(\frac{df}{dx}))[/itex] is a incline of this line
from the initial equation i got to this point and I'm not sure what to do next:
[tex]
\frac{f(x)}{x-x_0}=\tan(2\arctan(\frac{df}{dx}))
[/tex]
the initial equation i derived for determining the shape of the mirror is:
(assuming that light rays fall parallel to x-axis - light source is very far from the mirror)
f(x) is the shape I'm trying to determine
[tex]
x_0=-\frac{f(x)-\tan(2\arctan(\frac{df}{dx}))x}{\tan(2\arctan(\frac{df}{dx}))}
[/tex]
basicly this is an expression for a line passing through point [itex]x_0[/itex] and point on
f(x) where light reflected.
so [itex]\tan(2\arctan(\frac{df}{dx}))[/itex] is a incline of this line
from the initial equation i got to this point and I'm not sure what to do next:
[tex]
\frac{f(x)}{x-x_0}=\tan(2\arctan(\frac{df}{dx}))
[/tex]
Last edited: