Name the spherical mirror used as:
$(a)$ $1.$ Shaving mirror,
$2.$ Rear-view mirror in vehicles,
$3.$ Reflector in searchlights.
$(b)$ Write any three differences between a real and virtual image.

$(a)$ Draw a ray diagram in each of the following cases to show the position and nature of the image formed when an object is placed:
$(i)$ Between the focus and the centre of curvature of a concave mirror.
$(ii)$ Between the focus and the pole of a concave mirror.
$(iii)$ Between the centre of curvature and infinity for a concave mirror.
$(b)$ Give mathematical formulae for determining the magnification produced by a spherical mirror. What does $m = -1$ signify? Identify the mirror that can produce it.

Where is the image formed when an object is placed anywhere in front of a concave lens?

Where will the image be formed by a concave mirror when an object is placed between the pole and the focus point of the mirror?

The image formed by a lens is always erect and diminished. What is the nature of the lens?

The angle between an incident ray and the reflected ray is $70^{\circ}$ as shown in the figure. What is the value of $\theta$?