$A$ telescope has an objective of focal length $100 \ cm$ and an eyepiece of focal length $5 \ cm$. The least distance of distinct vision is $25 \ cm$. The telescope is focused for distinct vision on a scale $3 \ m$ away from the objective. The magnification produced is . . . . . .

$(a)$ $A$ 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 $3.8 \times 10^{8} \; m$.

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 $\,cm$)

If the tube length of an astronomical telescope is $96 \ cm$ and the magnifying power is $15$ for normal setting,then the focal length of the objective is . . . . . . $cm$.

The focal lengths of the objective lens and the eye lens of a Galilean telescope are $30\, cm$ and $3.0\, cm$ respectively. The telescope produces a virtual,erect image of an object situated far away from it at the least distance of distinct vision from the eye lens. In this condition,the magnifying power of the Galilean telescope should be:

In an astronomical telescope,the focal lengths of the objective lens and the eyepiece are $150 \, cm$ and $6 \, cm$ respectively. In the case where the final image is formed at the least distance of distinct vision,the magnifying power is: