If an object is placed between two plane mirrors inclined at an angle of $45^{\circ}$,then the number of images formed will be $9$. State whether this statement is True or False.

Draw ray diagrams showing the image formation by a concave mirror when an object is placed:
$(a)$ Between pole $(P)$ and focus $(F)$ of the mirror.
$(b)$ Between focus $(F)$ and centre of curvature $(C)$ of the mirror.
$(c)$ At centre of curvature $(C)$ of the mirror.
$(d)$ $A$ little beyond centre of curvature $(C)$ of the mirror.
$(e)$ At infinity.

State the sign convention used to measure the length of the image and the object.

$(a)$ What should be the position of the object,when a concave mirror is to be used $(i)$ as a shaving mirror,and $(ii)$ in torches producing a parallel beam of light? $(b)$ $A$ man standing in front of a mirror finds his image having a very small head and legs of normal size. What type of mirror is used in designing such a mirror?

$A$ ray of light enters from a medium with refractive index $n_1$ into a medium with refractive index $n_2$. If the angle of incidence is $\theta_1$ and the angle of refraction is $\theta_2$,then $\sin \theta_1 / \sin \theta_2 = \dots$

What is the nature of the final image formed by an astronomical telescope compared to the object?