How will you decide whether a given piece of glass is a convex lens,concave lens or a plane glass plate?

An object is placed $15\, cm$ from a convex mirror of radius of curvature $60\, cm$. Find the position of the image and its magnification.

Two lenses have powers of $(a) +2 \text{ D}$ and $(b) -4 \text{ D}$. Find the nature and focal length of each lens.

$(a)$ State the laws of refraction.
$(b)$ $A$ ray of light enters from a medium $A$ into a slab made up of a transparent substance $B$ (as shown in the figure). The refractive indices of medium $A$ and $B$ are $2.42$ and $1.65$ respectively. Complete the path of the ray of light until it emerges out of the slab.

$A$ child is standing in front of a magic mirror. She finds the image of her head bigger, the middle portion of her body of the same size, and that of the legs smaller. What is the order of combinations for the magic mirror from the top?

$(a)$ Write one use of a concave mirror as well as a convex mirror.
$(b)$ Draw ray diagrams for the following cases when a ray of light:
$(i)$ passing through the centre of curvature of a concave mirror is incident on it.
$(ii)$ parallel to the principal axis is incident on a convex mirror.
$(iii)$ is incident at the pole of a convex mirror.
$(iv)$ passing through the focus of a concave mirror is incident on it.