Question

You use 8x binoculars were used on a warbler (14cm long) in a tree 18cm away. What angle (in degrees) does the image of the warbler subtend on your retina?

Answer 1

Answer:

The angle it subtend on the retina is  $\theta_z = 0.44586^o$    

Explanation:

From the question we are told that

     The length of the warbler is  $L = 14cm = \frac{14}{100} = 0.14m$

      The distance from the binoculars is    $d = 18cm = \frac{18}{100} = 0.18m$

        The magnification of the binoculars is  $M =8$

Without the 8 X binoculars the  angle made with the angular size of the object  is mathematically represented as

          $\theta = \frac{L}{d}$

        $\theta = \frac{0.14}{0.18}$

           $= 0.007778 rad$

Now magnification can be represented mathematically as

         $M = \frac{\theta _z}{\theta}$

Where $\theta_z$ is the angle the image of the warbler subtend on your retina when the   binoculars i.e the  binoculars zoom.

So

      $\theta_z = M * \theta$

=>    $\theta_z =8 * 0.007778$

            $= 0.0622222224$

Generally the conversion to degrees can be mathematically evaluated as

             $\theta_z = 0.062222224 * (\frac{360 }{2 \pi rad} )$

              $\theta_z = 0.44586^o$