If the magnification of an image formed by a mirror is $(-\frac{1}{3})$,what type of mirror is it?

The figure shows a ray of light as it travels from medium $A$ to medium $B$. The refractive index of medium $B$ relative to medium $A$ is:

In torches,searchlights,and headlights of vehicles,the bulb is placed:

$(a)$ For the same angle of incidence $45^{\circ}$,the angle of refraction in two transparent media $I$ and $II$ is $20^{\circ}$ and $30^{\circ}$ respectively. Out of $I$ and $II$,which medium is optically denser and why?
$(b)$ Light enters from air to diamond,which has a refractive index of $2.42$. Calculate the speed of light in diamond,if the speed of light in air is $3.00 \times 10^{8} \text{ m s}^{-1}$.

An object $3 \, cm$ high is placed at a distance of $20 \, cm$ in front of a convex lens of focal length $12 \, cm$. Find the position,nature,and size of the image formed.

Draw ray diagrams showing the image formation by a convex lens when an object is placed:
$(a)$ Between optical centre and focus of the lens.
$(b)$ Between focus and twice the focal length of the lens.
$(c)$ At twice the focal length of the lens.
$(d)$ At infinity.
$(e)$ At the focus of the lens.