$A$ concave mirror of focal length $f$ (in air) is immersed in water $(\mu = 4/3)$. The focal length of the mirror in water will be

$A$ short straight object of height $100\, cm$ lies before the central axis of a spherical mirror whose focal length has absolute value $|f|=40\, cm$. The image of the object produced by the mirror is of height $25\, cm$ and has the same orientation as the object. One may conclude from the information:

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.

$A$ small linear object is placed on the optical axis of a concave mirror. If the distance of the nearest end of the object from the mirror is greater than the radius of curvature,then:

$A$ thin rod of length $f/3$ lies along the axis of a concave mirror of focal length $f$. One end of its magnified image touches an end of the rod. The length of the image is

$A$ 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.