PX158 - E2 - extended objects

\frac{π r^{2} S_{B} α^{2}}{l^{2}} = \frac{π D^{2} S_{B} α^{2}}{4 l^{2}} = \frac{π D^{2} S_{B} α^{2}}{4 α^{2} f^{2}} = \frac{π D^{2} S_{B}}{4 f^{2}} = \frac{π S_{B}}{4} \frac{1}{(\frac{f}{D})^{2}}

where, $\frac{f}{D} = f o c a l r a t i o$

angular magnification

α_{m i n} = 1.22 \frac{λ}{D}

eg: what is the minimum angular resolution of the human eye?
$α_{m i n} = 1.22 \frac{500 n m}{5 m m} = 0.000122 r a d \times \frac{180}{π r a d} \times 3600^{^{″}} = 25^{^{″}}$
- this is the limit, but more typical value $\approx 60^{^{″}}$
eg: what is the $α_{m i n}$ for the VLT?
$D = 8 m$
$α_{m i n} = {0.016}^{^{″}}$
for ground based telescopes, the atmospheric turbulence limits the angular resolution. this effect is called "seeing"
a good site will have "seeing" $= 1^{^{″}}$
adaptive optics can help correct this effect using deformable mirrors

measuring the 'blurring' due to earth's atmosphere (by bright stars and/or laser guide stars) and correct it via deformable mirrors (millisecond corrections)
telescopes are situated on high mountains to reduce these effects of earth's atmosphere
space telescopes do not suffer from this effect but they are very expensive to create, launch, and operate

m a g n i f i c a t i o n = \frac{α_{2}}{α_{1}} = \frac{f_{1}}{f_{2}}

eg: what is the angular magnification for celestron, $D = 90 m m$ , $f o c a l l e n g t h = 1250 m m$ , $e y e p i e c e = 32 m m$ ? what is the diffraction limit? $\frac{α_{1}}{α_{2}} = \frac{1250}{32} \approx 39$ $α_{m i n} = 1.22 \frac{λ}{D} = 1.22 \frac{500 n m}{90 m m} \approx 14^{^{″}}$