Which of the following always form a virtual image?

$(a)$ 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 $u$.

$A$ convex mirror always forms a virtual and erect image.

You are given water,mustard oil,glycerine,and kerosene. In which of these media would a ray of light incident obliquely at the same angle bend the most?

$A$ concave mirror and a convex lens are held in water. What changes, if any, do you expect in their focal length?

$(a)$ Define radius of curvature and focal length of a spherical mirror and show it on a figure.
$(b)$ Write the relation between the radius of curvature and the focal length of a spherical mirror.