if a monochromatic beam of light with a wavelength of 590 nanometers is traveling through air then enters a region of space where the index of refraction is 1.5, what will the light beam do? increase, decrease, or stay the same?

Answer 1

It slows down, shorter wavelength, same frequency

(note it can not change frequency. There is no storage of waves, the same number have to pass a given point per unit time on each side.)
lambda = V * T
so
lambda = V/f
if V goes down/ lambda goes down