As a monochromatic light ray passes from air
into water, two characteristics of the ray that will
not change are
(1) wavelength and period
(2) frequency and period
(3) wavelength and speed
(4) frequency and speed

The correct answer is

(2) frequency and period

In fact, when a light wave moves from one medium to another, its speed and its wavelength change. On the contrary, the frequency of the wave remains the same. Since the period is the reciprocal of the frequency:

this means that the period of the wave does not change neither. So, the correct answer is

(2) frequency and period