Question

State the condition under which a large magnification can be archived in an astronomical telescope.

Answer 1

According to the formula of magnifying power of a telescope, we have to conclude that focal length of objective lens must be much greater than eyepiece lens. Also the distance between these two lenses are a determining factor of magnifying power of astronomical telescopes.

Complete step by step solution:
In the image of an astronomical telescope, we can see that eyepiece lenses are those from which we are to see the far object, and object side lenses are objective lenses.

So, the magnification formula of astronomical telescope is $M=-\dfrac{{{f}_{0}}}{{{f}_{e}}}\left( 1+\dfrac{{{f}_{e}}}{d} \right).$
Where, ${{f}_{0}}$ is focal length of objective lens and ${{f}_{e}}$ is the focal length of eyepiece lens, $d$ is the distance between those two lenses.
Negative sign shows that the image is inverted.
So, we can conclude that for maximizing the magnitude of $M$, ${{f}_{0}}>>{{f}_{e}}$.
Also the diameter of the objective lens should be greater than the diameter of the eyepiece lens.

Additional Information:
Telescope, device used to form magnified images of distant objects. The telescope is undoubtedly the most important investigative tool in astronomy. It provides a means of collecting and analysing radiation from celestial objects, even those in the far reaches of the universe. It was invented by Galileo. Also, there are some names who claim that they discovered it earlier. A telescope made with lenses is called a refracting telescope. And a telescope that uses mirrors is called a reflecting telescope.

Note: Magnification of telescopes means how much the image of the object is magnified. It is the ratio of height of image to the height of the object. But it is too typical to calculate again and again for all the objects, so we derive the formula for magnifying power of a telescope with the factor of adjustment of lenses.