Answer:
x = 2 x 10¹⁶ Km
Explanation:
distance between two star,d = 10⁹ Km
separation between them, θ = 10⁻⁵ radians
focal length of the eyepiece = 1.5 cm = 0.015 m
focal length of the objective = 3 m
observer distance from star, x = ?
we know,
[tex]tan \theta = \dfrac{d}{x}[/tex]
for small angle
[tex]\theta = \dfrac{d}{x}[/tex].......(1)
angular magnification of telescope
[tex]M = \dfrac{f_{objective}}{f_{eyepiece}}=\dfrac{3}{0.015} = 200[/tex]
Angular magnification of the telescope is also calculated by
[tex]M = \dfrac{observed\ angle}{original\ angle}[/tex]
[tex]M = \dfrac{\theta_0}{\theta}[/tex]
now,
[tex]\dfrac{\theta_0}{\theta}=200[/tex]
[tex]\dfrac{\theta_0}{200}=\theta[/tex]
from equation (1)
[tex]\dfrac{\theta_0}{200}=\dfrac{d}{x}[/tex]
[tex]x=\dfrac{200d}{\theta_0}[/tex]
[tex]x=\dfrac{200\times 10^9}{10^{-5}}[/tex]
x = 2 x 10¹⁶ Km
Distance between the observer and the star is x = 2 x 10¹⁶ Km
