$A$ ray of light $AB$ parallel to the principal axis is incident on a convex lens as shown in the figure. Copy the figure.
$(i)$ Draw the refracted ray.
$(ii)$ Name the point through which the refracted ray passes on the principal axis.

For what position of the object does a concave mirror form a real and diminished image?

Describe the different cases of image formation by a convex lens. Provide the ray diagram for each case.

What is the lens placed near the eye in a compound microscope called?

$(a)$ Explain the following terms related to spherical lenses:
$(i)$ Optical centre
$(ii)$ Centres of curvature
$(iii)$ Principal axis
$(iv)$ Aperture
$(v)$ Principal focus
$(vi)$ Focal length
$(b)$ $A$ converging lens has a focal length of $12 \, cm$. Calculate at what distance should the object be placed from the lens so that it forms an image at $48 \, cm$ on the other side of the lens.

$(a)$ Calculate the distance at which an object should be placed in front of a convex lens of focal length $10\, cm$ to obtain a virtual image of double its size.
$(b)$ In the above given case,find the magnification,if the image formed is real. Express it in terms of the relation between $v$ and $u$.