For what position of the object does a convex lens form an erect and virtual image?

As the velocity of light increases,the refractive index of the medium decreases. Light enters from air to water having a refractive index of $4/3$. Find the speed of light in water. The speed of light in vacuum is $3 \times 10^{8} \text{ m s}^{-1}$.

$(a)$ 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.

$A$ ray of light is incident on a concave mirror after passing through the centre of curvature. What is the angle of incidence (in $°$)?

The refractive indices of medium $(1)$ and medium $(2)$ are $\eta_{1}$ and $\eta_{2}$ respectively,and the velocities of light in these media are $v_{1}$ and $v_{2}$ respectively. What is the formula to find the refractive index of medium $(2)$ with respect to medium $(1)$,denoted as $\eta_{21}$?

Name the type of lens that can be used to obtain:
$(i)$ $A$ magnified and virtual image.
$(ii)$ $A$ diminished and virtual image of the object.