Question

Two stars that are 109 km apart are viewed by a telescope and found to be separated by an angle of 10-5 radians. The eyepiece of the telescope has a focal length of 1.5 cm and the objective has a focal length of 3 meters.

Answer 1

Answer:

Distance between star and observer = 2 × $10^{16}$ km

Explanation:

Step 1

Angular magnification of telescope is given by formula:

             M = - f° ÷ fⁿ

where

M is angular magnification

f° is focal lens of object lens

fⁿ is  focal lens of eyepiece lens

Step 2

      M =  300cm ÷ 1.5 cm

           =  - 200 (-tive sign means image is inverted)

  M =  θⁿ ÷ θ°

   solve for θ°

  θ° =   θⁿ ÷ M

       =  $10^{-5}$ ÷  200

       = 5 × $10^{-10}$ radians

Step 3

now find distance between star and observer

  Adj = opposite ÷ θ°

         =  $10^{9}$ ÷ 5 × $10^{-10}$

         =  2 × $10^{16}$ km