$(a)$ 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.

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 $20 \text{ cm}$.

$A$ point object emits rays in all directions. Consider a ray emitted from the object that is parallel to the principal axis of the mirror. One of the points required to trace the reflected ray is the point of incidence itself,as shown in the figure. Select a point from the given figure through which the reflected ray passes.

$(a)$ Define the optical centre of a spherical lens.
$(b)$ You are given a convex lens of focal length $30 \, cm$. Where would you place an object to get a real,inverted,and highly enlarged image of the object? Draw a ray diagram showing the image formation.
$(c)$ $A$ concave lens has a focal length of $20 \, cm$. At what distance from the lens should an object be placed so that it forms an image at $15 \, cm$ away from the lens?

$(a)$ $A$ concave mirror produces a three times enlarged real image of an object placed at $10\, cm$ in front of it. Calculate the focal length of the mirror.
$(b)$ Show the formation of the image with the help of a ray diagram when an object is placed $6\, cm$ away from the pole of a convex mirror.

The images show the ray diagrams of images formed by convex mirrors. $P$ is the pole of the mirror. $C$ is the centre of curvature. $F$ is the focus. $AB$ is the object and $A'B'$ is the image.
$5$. Which statements are supported by the two diagrams? Circle 'Yes' or 'No' for each statement.

Is the statement supported by the two diagrams?	Yes/No
Convex mirrors produce virtual images	Yes/No
Convex mirrors produce erect images	Yes/No
Convex mirrors have their focus behind the mirrors	Yes/No

$6$. Which of these is a convex mirror?
$A$. Shaving mirror
$B$. Dentist’s mirror
$C$. Headlight mirror of a bike
$D$. Rear-view mirror of a car
$7$. A mirror magnifies the image of an object by $-1.5$ times. Which of the following is true about the image produced by the mirror?
$A$. The image is real and larger than the object.
$B$. The image is real and smaller than the object.
$C$. The image is virtual and larger than the object.
$D$. The image is virtual and smaller than the object.