An object is placed $20 \text{ cm}$ in front of a mirror. The image is formed at a distance of $15 \text{ cm}$. Determine the focal length and the type of mirror in each of the following cases: $(a)$ The image is formed in front of the mirror. $(b)$ The image is formed behind the mirror.

"$A$ 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.

Suppose you have three concave mirrors $A$, $B$ and $C$ of focal lengths $10 \text{ cm}$, $15 \text{ cm}$ and $20 \text{ cm}$ respectively. For each concave mirror, you perform an experiment of image formation for three object distances of $10 \text{ cm}$, $20 \text{ cm}$ and $30 \text{ cm}$. Giving reasons, answer the following:
$(a)$ For the three object distances, identify the mirror$(s)$ which will form an image of magnification $m = -1$.
$(b)$ Out of the three mirrors, identify the mirror which would be preferred for shaving or makeup purposes.
$(c)$ For mirror $B$, draw the ray diagrams for image formation for object distances $10 \text{ cm}$ and $20 \text{ cm}$.

$A$ concave mirror and a convex lens are held in water. What changes, if any, do you expect in their focal length?

Both a spherical mirror and a thin spherical lens have a focal length of $-15 \; cm$. What type of mirror and lens are they?

The image shows the path of light as it travels from one medium to another.
$(9)$ What are medium $1$ and medium $2$?

	Medium $1$	Medium $2$
$A$.	Water	Kerosene
$B$.	Kerosene	Diamond
$C$.	Flint glass	Water
$D$.	Kerosene	Flint glass

$(10)$ The power of a lens $(P)$ is calculated by the formula, $P = \frac{1}{f}$, where $f$ is the focal length of the lens in meters. A lens has a focal length of $-0.25 \ m$. Is it a convex lens or a concave lens? Explain your answer.