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?

The angle it subtend on the retina is      

Explanation:

From the question we are told that

     The length of the warbler is  

      The distance from the binoculars is    

        The magnification of the binoculars is  

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

         

       

           

Now magnification can be represented mathematically as

         

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

So

     

=>    

           

Generally the conversion to degrees can be mathematically evaluated as

             

               

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