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Monochromatic light of wavelength $589 \mathrm{~nm}$ is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light? Refractive index of water is $1.33$.
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(a) For reflected light, wavelength, frequency and speed remains same as incident light. $\lambda=589 \mathrm{~nm}, \mathrm{c}=3 \times 10^8 \mathrm{~ms}^{-1}$. $v=\frac{\mathrm{c}}{\lambda}=\frac{3 \times 10^8}{589 \times 10^{-9}}=5.09 \times 10^{14} \mathrm{~Hz}$
(b) For refracted light the frequency of the refracted light is the same as the incident frequency. The speed changes due to change in wavelength.
$\because \mathrm{n}=1.33$
$\therefore v=\frac{\mathrm{c}}{\lambda}=\frac{3 \times 10^8}{1.33}=2.26 \times 10^8 \mathrm{~ms}^{-1}$.
Wavelength, $\lambda=\frac{\mathrm{v}}{\mathrm{v}}=\frac{2.26 \times 10^8}{5.09 \times 1014}$ $=0.444 \times 10^{-6}=444 \times 10^{-9} \mathrm{~m}
(b) For refracted light the frequency of the refracted light is the same as the incident frequency. The speed changes due to change in wavelength.
$\because \mathrm{n}=1.33$
$\therefore v=\frac{\mathrm{c}}{\lambda}=\frac{3 \times 10^8}{1.33}=2.26 \times 10^8 \mathrm{~ms}^{-1}$.
Wavelength, $\lambda=\frac{\mathrm{v}}{\mathrm{v}}=\frac{2.26 \times 10^8}{5.09 \times 1014}$ $=0.444 \times 10^{-6}=444 \times 10^{-9} \mathrm{~m}
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