Monochromatic light of wavelength $589 \; nm$ is incident from air on a water surface. What are the wavelength,frequency,and speed of
$(a)$ reflected,and
$(b)$ refracted light? Refractive index of water is $1.33$.

(N/A) Wavelength of incident monochromatic light,$\lambda = 589 \; nm = 589 \times 10^{-9} \; m$.
Speed of light in air,$c = 3 \times 10^{8} \; m/s$.
Refractive index of water,$\mu = 1.33$.
$(a)$ The ray reflects back into the same medium (air). Therefore,the wavelength,speed,and frequency of the reflected ray remain the same as the incident ray.
Frequency of light is given by $v = \frac{c}{\lambda} = \frac{3 \times 10^{8}}{589 \times 10^{-9}} \approx 5.09 \times 10^{14} \; Hz$.
Thus,for reflected light: Speed $= 3 \times 10^{8} \; m/s$,Frequency $= 5.09 \times 10^{14} \; Hz$,Wavelength $= 589 \; nm$.
$(b)$ Frequency of light is independent of the medium. Thus,the frequency of the refracted ray in water is the same as the incident light: $v = 5.09 \times 10^{14} \; Hz$.
Speed of light in water is $v_{w} = \frac{c}{\mu} = \frac{3 \times 10^{8}}{1.33} \approx 2.26 \times 10^{8} \; m/s$.
Wavelength in water is $\lambda_{w} = \frac{v_{w}}{v} = \frac{2.26 \times 10^{8}}{5.09 \times 10^{14}} \approx 444.01 \times 10^{-9} \; m = 444.01 \; nm$.