Why does the focal length of a lens increase when it is put in water?
Light changes direction when it goes from one medium to another for two reasons. One is because it is a wave and other is because the light travels different speeds in the two mediums.
Light travels the speed c in vacuum and it travels the slower speed 3/4c in water and even the slower speed 2/3c in glass.
When the lens is in air the difference in speed is 2/3c versus c. When it is in water the difference in speed is 2/3c versus 3/4c. The difference in speed is smaller when it is in water and so the light bends less. The light bending less corresponds to a longer focal length.