The focal lengths of the lenses of an astronomical telescope are $50\, cm$ and $5\, cm$. The length of the telescope when the image is formed at the least distance of distinct vision is

An astronomical refracting telescope is being used by an observer to observe planets in normal adjustment. The focal lengths of the objective and eyepiece used in the construction of the telescope are $20\,m$ and $2\,cm$ respectively. Consider the following statements about the telescope:
$(a)$ The distance between the objective and eyepiece is $20.02\,m$.
$(b)$ The magnification of the telescope is $1000$.
$(c)$ The image of the planet is erect and diminished.
$(d)$ The aperture of the eyepiece is smaller than that of the objective.
The correct statements are:

The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index $1.5$. When the telescope is adjusted to infinity, the separation between the two lenses is $16 \,cm$. If the space between the lenses is now filled with water and the telescope is again adjusted for infinity, then the present separation between the lenses is: (in $\,cm$)

An astronomical refracting telescope has an objective of focal length $20 \, m$ and an eyepiece of focal length $2 \, cm$. Then:

All of the following statements are correct except:

The focal length of the objective of an astronomical telescope is $1.5 \ m$. Under normal adjustment,the length of the telescope is $1.56 \ m$. The focal length of the eyepiece is: (in $m$)