Question

The magnifying power of an astronomical telescope is $8$, then the ratio of the focal length of the objective to the focal length of the eyepiece is:
\[(A)8\]
\[(B)\dfrac{1}{8}\]
\[(C)0.45\]
\[(D){\text{None of these}}\]

Answer 1

Hint: Magnification power is the amount that defines how much an instrument that can enlarge an object. Find the formula of the magnifying power of the astronomical telescope, you will find the required ratio by putting the value given in the problem.

Formula used:
\[{\text{Magnifying power = }}\dfrac{{{\text{focal length of the objective}}}}{{{\text{focal length of the eye piece}}}}\]

Complete step by step answer:
A telescope is generally of two types – Astronomical telescope and Terrestrial telescope. The stars of the sky are observed by the Astronomical telescope. In this case, the final image is inverse according to the object.
Magnification power is the amount that defines how much an instrument that can enlarge an object. This has a direct relationship with the focal length. The magnification or the magnifying power also changes when the eyepiece changes.
The magnifying power of the telescope is defined as the ratio of the focal length of the objective and the focal length of the eyepiece i.e.
\[{\text{Magnifying power = }}\dfrac{{{\text{focal length of the objective}}}}{{{\text{focal length of the eye piece}}}}\]
Here we are asked the ratio of the focal length of the objective to the focal length of the eyepiece.
Given, The magnifying power of an astronomical telescope is $8$.
\[\therefore {\text{Magnifying power = 8 = }}\dfrac{{{\text{focal length of the objective}}}}{{{\text{focal length of the eye piece}}}}\]
So the amount is $8$ .

Hence the right answer is In option A, 8.

Note: The telescope is structural of two types: a Refracting telescope and a Reflecting telescope. In the Refracting telescope, the objective is made up of one or more lenses. In the Reflecting telescope, big concave or parabolic mirrors are used as the objective.
Nowadays many types of telescopes are used like Radio Telescope, Infrared Telescope, X-ray Telescope, High energy Telescope, and Gravitational-wave Telescope.