Light enters from air into diamond,which has a refractive index of $2.42$. Calculate the speed of light in diamond. The speed of light in air is $3.0 \times 10^{8} \text{ m s}^{-1}$.

$(a)$ 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.

What is meant by the power of a lens? Give its $SI$ unit. When two or more lenses are placed in contact,what will be their combined power?

If the absolute refractive indices of water and glass are $\frac{4}{3}$ and $\frac{3}{2}$ respectively,then what will be the ratio of the velocity of light in water to that of glass?

The power of a lens is $5$ dioptre. What is the focal length of the lens (in $m$)?

$A$ full-length image of a distant tall building can definitely be seen by using: