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

$A$ concave mirror of focal length $10 \, cm$ is immersed in water $(\mu = 4/3)$. The new focal length will be ...... $cm$.

$A$ concave mirror of focal length $15\, cm$ forms an image having twice the linear dimensions of the object. The position of the object when the image is virtual will be........$cm$

Assertion : The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason : Laws of reflection are strictly valid for plane surfaces,but not for large spherical surfaces.

$A$ boy stands $30 \,cm$ in front of a mirror. The height of his erect image is $1/5 \,th$ of his actual height. The mirror used is ..... .

An object is placed at $(i) \; 10 \; cm$,$(ii) \; 5 \; cm$ in front of a concave mirror of radius of curvature $15 \; cm$. Find the position,nature,and magnification of the image in each case.