A concave mirror having focal length 'f' is immersed in water. What will be its new focal length?

The focal length remains the same.
As we know, the focal length of a concave mirror is determined by the formula:
$\mathrm{f}=\frac{\mathrm{R}}{2}$  (R is the radius of curvature)
So, we can see that the focal length of a concave mirror is dependent only on the radius of curvature and has nothing to do with the external medium.
Therefore, the focal length of the concave mirror will remain the same in water also.