Question

The angular separation of the two components of a double star is 0.6 microradians, and the light from the double star has a wavelength of 471 nm. What is the diameter (in cm) of the smallest telescope mirror that will resolve the double star?

Answer 1

Answer:

Diameter, d = 95.7 cm

Explanation:

It is given that,

Angular separation of the two components of a double star is, $\theta=0.6\ \mu\ radian=0.6\times 10^{-6}\ rad$

Wavelength of double star, $\lambda=471\ nm=471\times 10^{-9}\ m$

Let d is the diameter of the smallest telescope mirror that will resolve the double star. The formula for the angular separation is given by :

$\theta=\dfrac{1.22\lambda}{d}$

$d=\dfrac{1.22\lambda}{\theta}$

$d=\dfrac{1.22\times 471\times 10^{-9}}{0.6\times 10^{-6}}$

$d=0.957\ m$

or

d = 95.7 cm

So, the diameter of the smallest telescope mirror that will resolve the double star is 95.7 cm. Hence, this is the required solution.