Question

The objective of an astronomical telescope is a convex lens of _______ focal length.

Answer 1

Hint:Recall the basics of the astronomical telescopes. We have asked about the focal length of the convex lens used in the astronomical telescope. So, we should first determine whether the objective lens or eyepiece lens in the telescope is a convex lens. Then using the formula for the magnification of the telescope derive the relation between the magnification of the telescope and focal length of the objective lens and fill the blank.

Formula used:
The magnification $$m$$ of a telescope is given by
$$m={\displaystyle \frac{f_o}{f_e}}$$ …… (1)
Here, $$f_o$$ is the focal length of the objective lens and $$f_e$$ is focal length of the eyepiece lens.

Complete answer:
We have asked about the focal length of the convex lens used in the astronomical focal length.We need to determine whether the convex lens used in the astronomical telescope is either an objective lens or eyepiece lens.We know that when the light from an astronomical object enters the telescope, the objective lens in the telescope collects this light and focuses it to the focal point in order to magnify the image of the astronomical object and the eyepiece lens then collects this light from the focal point and forms the magnified image on the retina of the human eye.

The objective lens converges the light from the astronomical object to the focal point which shows that this objective lens must be a converging or convex lens.Let us now determine what should be the focal length of the convex objective lens used in the telescopes.From equation (1), we can conclude that the magnification of the telescope is directly proportional to the focal length of the objective lens. Hence, the focal length of the convex lens used in the astronomical telescopes must be larger.

Hence, the objective of an astronomical telescope is a convex lens of larger focal length.

Note: The students should be careful while determining whether the convex lens used in the telescope is either an objective lens or eyepiece lens. If one fails to correctly determine the type of lens then according to the formula for magnification of the telescope, one can result with the incorrect solution. Hence, the type of lens should be correctly determined.