Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of

(i) reflected and

(ii) refracted light? (µ of water is 1.33).

Here, wavelength λ = 589nm

c = 3 x ${{10}^{8}}$ m/s

µ = 1.33

(i) For reflected light,

Wavelength, λ = 589nm = 589 x ${{10}^{-9}}$ m

v = c/λ = 3 x ${{10}^{8}}$ / 589 x ${{10}^{-9}}$

= 5.09 x ${{10}^{14}}$ Hz

Speed, v=c=3 x ${{10}^{8}}$ m/s

(ii) For refracted light,

λ’ = λ/µ = 589 x ${{10}^{-9}}$/1.33 = 4.42 x ${{10}^{-7}}$ m

As frequency remains unaffected on entering another medium therefore

v’ = v = 5.09 x ${{10}^{14}}$ Hz

speed, v’ = c/µ = 3 x ${{10}^{8}}$/1.33

=2.25 x ${{10}^{8}}$ m/s