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

Distance between star and observer = 2 ×
`10^(16)` km

Step-by-step 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