What would your image look like if you stood close to a large:
$(a)$ Convex mirror?
$(b)$ Concave mirror?
Give reasons for your answer.

$(a)$ If the image formed by a lens is diminished in size and erect, for all positions of the object, what type of lens is it?
$(b)$ Name the point on the lens through which a ray of light passes undeviated.
$(c)$ An object is placed perpendicular to the principal axis of a convex lens of focal length $20 \text{ cm}$. The distance of the object from the lens is $30 \text{ cm}$. Find:
$(i)$ The position of the image.
(ii) The magnification.
(iii) The nature of the image formed.

$(i)$ 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.

Study the following table for a convex lens for different positions of the object and answer the following questions:

Position of object	Position of image	Relative size of image
At infinity	At focus $F_2$	Highly diminished, point-sized
Beyond $2F_1$	Between $F_2$ and $2F_2$	Diminished
At $2F_1$	At $2F_2$	Same size
Between $F_1$ and $2F_1$	Beyond $2F_2$	Enlarged
At focus $F_1$	At infinity	Infinitely large or highly enlarged
Between focus $F_1$ and optical centre $O$	On the same side of the lens as the object	Enlarged

$(i)$ What is the nature of the image if an object is placed at infinity?
(ii) Identify the nature of the image when the object is between the focus and the optical centre.
(iii) What is the position of the image when the object is placed at focus $F_1$?
(iv) What is the focal length of a lens for an object placed $50 \text{ cm}$ from the lens producing a virtual image at a distance of $10 \text{ cm}$ in front of the lens?

$(a)$ 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.

$(i)$ To construct a ray diagram, we use two light rays chosen such that their directions after reflection from the mirror are easily determined. List these two rays and state their paths after reflection. Use these two rays to locate the image of an object placed between infinity and the centre of curvature of a concave mirror.
(ii) Draw a ray diagram to show the formation of an image of an object placed between the pole and the principal focus of a concave mirror. How will the nature and size of the image change if the mirror is replaced by a converging lens of the same focal length?