An object $2.5 \, cm$ high is placed at a distance of $10 \, cm$ from a concave mirror of radius of curvature $30 \, cm$. The size of the image is ........ $cm$.

$A$ point object is placed at a distance of $30 \, cm$ from a convex mirror of focal length $30 \, cm$. The image will form at

Write the relationship between the radius of curvature and the focal length for a spherical mirror.

$A$ candle flame of $3 \, cm$ is placed at $300 \, cm$ from a wall. $A$ concave mirror is kept at distance $x$ from the wall in such a way that the image of the flame on the wall is $9 \, cm$. Then $x$ is......$cm$.

An object of length $f/3$ is placed on the principal axis of a concave mirror of focal length $f$. The image of the end of the object farthest from the mirror is formed at the same position. Find the length of the image.

$A$ concave mirror forms a real image three times larger than the object on a screen. The object and screen are moved until the image becomes twice the size of the object. If the shift of the object is $6 \ cm$,find the shift of the screen and the focal length of the mirror.