The velocity of light in a vacuum is $....$

$(a)$ 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.

$(a)$ Why does a ray of light passing through the centre of curvature of a concave mirror after reflection get reflected back along the same path?
$(b)$ Why are convex mirrors commonly used as rear-view mirrors in vehicles?
$(c)$ $A$ pencil partly immersed in water in a glass tumbler appears to be displaced at the interface of air and water. Name the phenomenon of light responsible for it.

The radius of curvature of a spherical mirror is half of the focal length.

The size of an image of an object formed by a mirror with a focal length of $20\, cm$ is observed to be reduced to $1/3^{rd}$ of its size. At what distance is the object placed from the mirror? What is the nature of the image and the mirror?

If a convex lens forms a real and magnified image of an object,where is the object placed?