There are four convex lenses $L_{1}, L_{2}, L_{3}$ and $L_{4}$ with focal lengths $2 \ cm, 4 \ cm, 6 \ cm$ and $8 \ cm$ respectively. Two of these lenses form a telescope of length $10 \ cm$ and magnifying power $4$. The objective and eye lenses are respectively:

When the diameter of the aperture of the objective of an astronomical telescope is increased,its

$(a)$ $A$ giant refracting telescope at an observatory has an objective lens of focal length $15 \; m$. If an eyepiece of focal length $1.0 \; cm$ is used,what is the angular magnification of the telescope?
$(b)$ If this telescope is used to view the moon,what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is $3.48 \times 10^{6} \; m$,and the radius of the lunar orbit is $3.8 \times 10^{8} \; m$.

All of the following statements are correct except:

On which of the following does the magnifying power of a telescope depend?

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 $\,cm$)