Question

The focal length of concave mirror is safe is there any change in focal length when it is completely immersed in water if not why

Answer 1

There will be no change in the focal length of the concave mirror because unlike image and object distance, focal length cannot be changed.

Answer 2

If it reflects from the back surface, then the focal length can change slightly, depending on the thickness of the glass.

If it reflects from the front surface, then the focal length doesn't change, because (unlike a lens) no refraction is involved in the determination of the focal length.