Question

What will be the minimum angular separation between two stars when a telescope is used to observe them with an objective having a circular aperture $20cm$? It has been mentioned that the wavelength of light used will be $5900\overset{0}{\mathop{A}}\,$.

Answer 1

Hint: The minimum angle of separation can be found by taking the ratio of the $1.22$ times the wavelength of the light to the radius of the circular aperture. The radius of the circular aperture and acceleration due to gravity has been given in the question. Substitute the values in it. This will help you in answering this question.

Complete answer:
First of all let us mention the parameters mentioned in the question. The radius of circular aperture of the objective of the telescope will be given as,
$a=20cm=0.2m$
The wavelength of the light used in this experiment can be written as,
$\lambda =5900\overset{0}{\mathop{A}}\,=5.9\times {{10}^{-7}}m$
The minimum angle of separation can be found by taking the ratio of the $1.22$ times the wavelength of the light to the radius of the circular aperture. This can be written as an equation given as,
$d\theta =\dfrac{1.22\lambda }{a}$
Substituting the values in the equation will give,
$d\theta =\dfrac{1.22\times 5.9\times {{10}^{-7}}}{0.2}=3.599\times {{10}^{-6}}rad$
Therefore the minimum angle of separation between the two stars mentioned as in the question will be given as,
$d\theta =3.599\times {{10}^{-6}}rad$
Hence the answer for the question has been calculated.

Note:
A telescope is defined as an optical device working with the help of curved mirrors, lenses, or a combination of both to observe distant bodies or various equipment helpful in observing distant bodies by their emission, absorption, or reflection of the electromagnetic radiation. The refracting telescopes are the first known practical telescopes which were invented at the beginning of the seventeenth century in the Netherlands with the usage of the glass lenses.