Complete Question
Due to blurring caused by atmospheric distortion, the best resolution that can be obtained by a normal, earth-based, visible-light telescope is about 0.3 arcsecond (there are 60 arcminutes in a degree and 60 arcseconds in an arcminute).Using Rayleigh's criterion, calculate the diameter of an earth-based telescope that gives this resolution with 700 nm light
Answer:
The diameter is [tex]D = 0.59 \ m[/tex]
Explanation:
From the question we are told that
The best resolution is [tex]\theta = 0.3 \ arcsecond[/tex]
The wavelength is [tex]\lambda = 700 \ nm = 700 *10^{-9 } \ m[/tex]
Generally the
1 arcminute = > 60 arcseconds
=> x arcminute => 0.3 arcsecond
So
[tex]x = \frac{0.3}{60 }[/tex]
=> [tex]x = 0.005 \ arcminutes[/tex]
Now
60 arcminutes => 1 degree
0.005 arcminutes = > z degrees
=> [tex]z = \frac{0.005}{60 }[/tex]
=> [tex]z = 8.333 *10^{-5} \ degree[/tex]
Converting to radian
[tex]\theta = z = 8.333 *10^{-5} * 0.01745 = 1.454 *10^{-6} \ radian[/tex]
Generally the resolution is mathematically represented as
[tex]\theta = \frac{1.22 * \lambda }{ D}[/tex]
=> [tex]D = \frac{1.22 * \lambda }{\theta }[/tex]
=> [tex]D = \frac{1.22 * 700 *10^{-9} }{ 1.454 *10^{-6} }[/tex]
=> [tex]D = 0.59 \ m[/tex]
