Question

Using Rayleigh's criterion, calculate the diameter of an earth-based telescope that gives this resolution with 700 nm light.

Answer 1

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  $D = 0.59 \ m$    

Explanation:

From the question we are told that

      The best resolution is  $\theta = 0.3 \ arcsecond$

       The  wavelength is  $\lambda = 700 \ nm = 700 *10^{-9 } \ m$

       

Generally the

         1 arcminute  = >  60 arcseconds

=>      x arcminute =>   0.3 arcsecond

So

       $x = \frac{0.3}{60 }$

=>    $x = 0.005 \ arcminutes$

Now

         60 arcminutes  =>  1 degree

          0.005 arcminutes = >  z degrees  

=>       $z = \frac{0.005}{60 }$

=>      $z = 8.333 *10^{-5} \ degree$

Converting to radian  

           $\theta = z = 8.333 *10^{-5} * 0.01745 = 1.454 *10^{-6} \ radian$

Generally the resolution is mathematically represented as

            $\theta = \frac{1.22 * \lambda }{ D}$

=>    $D = \frac{1.22 * \lambda }{\theta }$

=>     $D = \frac{1.22 * 700 *10^{-9} }{ 1.454 *10^{-6} }$    

=>     $D = 0.59 \ m$