Question

With the help of a telescope that has an objective of diameter 200cm, it is proved that light of wavelengths of the order of $6400{A^0}$ coming from a star can be easily resolved, Then the limit of resolution is
(A). $39 \times {10^8}\deg$
(B). $39 \times {10^8}rad$
(C). $19.5 \times {10^8}rad$
(D). $19.5 \times {10^8}\deg$

Answer 1

Hint- Before solving this we will go through the resolving power and then we will use the required formula for calculating the resolving power of this telescope .It is defined as the inverse of distance or angular separation between two objects that can only be determined when the optical instrument is seen.

Complete step-by-step solution -
A telescope's ability to distinguish very close objects is its resolving power. The resolving power of a telescope is the ability to differentiate (i.e. to appear as distinct) points from an object at a small angular distance or to classify objects from far away, which are nearby and separating them into individual images, by an optical instrument.
Formula to calculate resolving power $\theta = \dfrac{1.220 \lambda}{D}$.
Where
$\theta$ is the angular resolution,
$\lambda$ is the wavelength of light,
And D is the diameter.
Now limit of resolution is given by
$\theta = \dfrac{{1.22 \times {\text{wavelength of light}}}}{{{\text{diameter of objective}}}} \\\ \Rightarrow \theta = \dfrac{{1.22 \times \lambda }}{D} \\\ \Rightarrow \theta = \dfrac{{1.22 \times 6400 \times {{10}^{ - 10}}}}{{200 \times {{10}^{ - 2}}}} \\\ \Rightarrow \theta = 39 \times {10^{ - 8}}rad \\\$
Hence, the correct option is “D”.

Additional Information-
Human beings have been looking up at the stars for centuries and asking what's out there. The topic has generally been put to philosophers and theologians for much of human history. We were only able to look deeper at our many world’s problems with the invention of the optical telescope.
A telescope is an instrument that captures and concentrates light (or electromagnetic waves). A telescope that detects the visible (or visual) portion of the electromagnetic spectrum is an optical telescope.

Note- Thus higher the diameter d, better the resolution. The best astronomical optical telescopes have mirror diameters as large as 10m to achieve the best resolution. Larger wavelengths also reduce the resolution power and therefore large mirrors are required for radio and microwave telescopes.