Question

For red light (λ = 0.64 µm), the imaginary part of the refractive index (ni) in pure water is approximately 1.3×10-8 ; for blue light (λ = 0.48 µm), ni ≈ 1.0×10-9 . The deep end of a typical home swimming pool is approximately 2.5 meters deep. Compute the fraction of each wavelength that survives the two-way trip to the bottom of the pool and back, when illuminated (and viewed) directly from above. In light of your findings (and considering the appearance of most swimming pools when viewed from the air), comment on the common assumption that water is ‘colorless’.

Answer 1

_r = 0.64 um ,

= 0.64 X 10^-6 m

n_i = 1.3 X 10^-8

_b = 0.48 um

= 0.48 X 10^-6 m

n_i = 1.0 X 10^-9  

x = 2 X 2.5 m = 05 m

F/F_o for red = exp ( - 4 X 1.3 X10^-8 X 5 / 0.64 X 10^-6 )

= 0.28

and sameway for blue is

F/F_o for blue = exp ( - 4 X 1 X 10^-9 X 5 / 0.64 X 10^-6 )

= 0.88

the transmission of the 88% is going to oppose 28 % of the red colour this is the reason why the water will

appear in red colour.

Assumption is based on like the water flow from faucet and also glass of water, when the path length of water is

short.

if x is small and get 100 % transmission this appears colourless.