In which of the following,the image of an object placed at infinity will be highly diminished and point-sized?

$(a)$ 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.

$(a)$ The refractive index of diamond is $2.42$. What is the meaning of this statement?
$(b)$ Redraw the diagram given below in your answer book and complete the path of the ray.
$(c)$ What is the difference between virtual images produced by concave and convex mirrors?
$(d)$ What does the negative sign in the value of magnification produced by a mirror indicate about an image?

How will you decide whether a given piece of glass is a convex lens,concave lens,or a plane glass plate?

$(i)$ Define the principal focus of a concave mirror.
$(ii)$ Why do we prefer a convex mirror as a rear-view mirror in vehicles?
$(iii)$ We wish to obtain an erect image of an object using a convex lens. Draw a ray diagram to show the image formation in this case.

Draw the ray diagram in each case to show the position,nature,and size of the image formed when the object is placed:
$(i)$ At the centre of curvature of a concave mirror.
$(ii)$ Within the focal length of a convex lens.
$(iii)$ Between the pole and focus of a concave mirror.
$(iv)$ In front of a convex mirror.
$(v)$ In front of a concave lens.