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, $\lambda =589nm=589\times {10}^{-9}m$
a) $f_a=\frac{C}{\lambda }=\frac{3\times {10}^8}{589\times {10}^{-9}}=5.09\times {10}^{14}{\sec }^{-1}[\because f=\frac{c}{\lambda }]$

b) $\frac{{\mu }_a}{{\mu }_w}=\frac{{\lambda }_w}{{\lambda }_a}\Rightarrow \frac{1}{1.33}=\frac{{\lambda }_w}{589\times {10}^{-9}}\Rightarrow {\lambda }_w=443nm$

c) $f_w=f_a=5.09\times {10}^{14}se{c}^{-1}$ [ frequency does not change ]

d) $\frac{{\mu }_a}{{\mu }_w}=\frac{v_w}{v_a}\Rightarrow v_w=\frac{{\mu }_a{v}_a}{{\mu }_w}=\frac{3\times {10}^8}{1.33}=2.25\times {10}^{8}m/sec$.