Question

The wavelength of sodium light in air is 589 nm. (a) Find its frequency in air. (b) Find its wavelength in water (refractive index = 1.33). (c) Find its frequency in water. (d) Find its speed in water.

Answer 1

Given that, for sodium light,
$1=589nm=589\times {10}^{-9}m\left(a\right)f_a=\frac{3\times {10}^8}{589\times {10}^{-9}}=5.09\times {10}^{14}se{c}^{-1}\left(b\right)\frac{{\mu }_a}{{\mu }_w}=\frac{{\lambda }_w}{{\lambda }_q}\Rightarrow \frac{1}{1.33}=\frac{{\lambda }_w}{589\times {10}^{-9}}\Rightarrow {\lambda }_w=443nm\left(c\right)f_w=f_a=5.09\times {10}^{14}se{c}^{-1}Rightarrow{v}_w=\frac{{\mu }_a{v}_a}{{\mu }_w}=\frac{3\times {10}^8}{\left(1.33\right)}=2.25\times {10}^{8}m/sec.$