When an object is placed $20 \text{ cm}$ from a concave mirror, a real image magnified three times is formed. Find:
$(a)$ The focal length of the mirror.
$(b)$ Where must the object be placed to give a virtual image three times the height of the object (in $\text{ cm}$)?

"$A$ convex lens can form a magnified erect as well as magnified inverted image of an object placed in front of it." Draw ray diagrams to justify this statement, stating the position of the object with respect to the lens in each case. An object of height $4 \text{ cm}$ is placed at a distance of $20 \text{ cm}$ from a concave lens of focal length $10 \text{ cm}$. Use the lens formula to determine the position of the image formed.

No matter how far you stand from a mirror,your image appears erect. The mirror is likely to be

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 the object is placed:
$(i)$ between optical centre and principal focus $(F)$ of a convex lens.
$(ii)$ between $F$ and $2F$ of a convex lens.
$(iii)$ at $2F$ of a convex lens.
$(b)$ How will the nature and position of the image formed change in case $(i)$ and $(ii)$ in part $(a)$ of this question if the lens is replaced by a concave lens? Draw the corresponding ray diagram.

For which type of mirror will the image always be erect,regardless of the distance at which the object is placed?