$A$ concave mirror of focal length $f$ in air is dipped in a liquid of refractive index $\mu$. Its focal length in the liquid will be $:$

In a car,a rear-view mirror having a radius of curvature $1.50 \, m$ forms a virtual image of a bus located $10.0 \, m$ from the mirror. The factor by which the mirror magnifies the size of the bus is close to

$A$ concave shaving mirror has a radius of curvature of $35.0 \, cm$. It is positioned so that the upright image of a man's face is $2.5 \, \times$ the size of the face. How far is the mirror from the face in $cm$?

$A$ small linear object of length $b$ is placed on the axis of a concave mirror of focal length $f$ at a distance $u$ from its pole. What is the approximate length of the image?

$A$ small candle,$2.5\; cm$ in size,is placed at $27\; cm$ in front of a concave mirror of radius of curvature $36\; cm$. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror,how would the screen have to be moved?

$STATEMENT-1$: 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. because
$STATEMENT-2$: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.