cyfrinairw7pr

2023-02-21

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

Caltolmsn

Given that, for sodium light,
$1=589nm=589×{10}^{-9}m$(a)${f}_{a}=\frac{3×{10}^{8}}{589×{10}^{-9}}\phantom{\rule{0ex}{0ex}}=5.09×{10}^{14}{\mathrm{sec}}^{-1}$(b)$\frac{\mu a}{\mu w}=\frac{{\lambda }_{w}}{{\lambda }_{q}}\phantom{\rule{0ex}{0ex}}⇒\frac{1}{1.33}=\frac{\lambda w}{589×{10}^{-9}}\phantom{\rule{0ex}{0ex}}⇒{\lambda }_{w}=443nm$(c)${f}_{w}={f}_{a}\phantom{\rule{0ex}{0ex}}=5.09×{10}^{14}se{c}^{-1}\phantom{\rule{0ex}{0ex}}⇒{v}_{w}=\frac{{\mu }_{a}{v}_{a}}{{\mu }_{w}}\phantom{\rule{0ex}{0ex}}=\frac{3×108}{\left(1.33\right)}=2.25×{10}^{8}m/sec.$

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