The two stars in a binary star system have an angular separation of 1.0 × 10^-5 rad.If the wavelength of the light from the system is 500 nm,what is the smallest diameter aperture telescope that could just resolve this system to show that it contains two stars? A)0.50 cm B)0.61 cm C)5.0 cm D)6.1 cm

Question

Quizplus · Accepted Answer

The angular resolution of a telescope is given by:
$	heta = 1.22 \frac{\lambda}{D}$

Where,
$	heta$ is the angular resolution
$\lambda$ is the wavelength of light
$D$ is the diameter of the aperture

We know that the angular separation of the stars is $	heta = 1.0 	imes 10^{-5}$ rad and the wavelength of the light is $\lambda = 500$ nm.

Substituting these values in the above formula, we get:

$1.0 	imes 10^{-5} = 1.22 \frac{500 	imes 10^{-9}}{D}$

Solving for $D$, we get:

$D = \frac{1.22 	imes 500 	imes 10^{-9}}{1.0 	imes 10^{-5}} = 6.1$ cm

Therefore, the smallest diameter aperture telescope that could just resolve this system to show that it contains two stars is 6.1 cm.

The Two Stars in a Binary Star System Have an Angular