Subjective Type

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.

Solution

Given that, for sodium light, $$\lambda=589\ nm=589\times 10^{-9}\ m$$
a) $$f_a=\dfrac C\lambda=\dfrac{3\times 10^8}{589\times 10^{-9}}=5.09\times 10^{14}\sec^{-1}\left[ \because f=\dfrac{c}{\lambda}\right]$$

b) $$\dfrac{\mu_a}{\mu_w}=\dfrac{\lambda_w}{\lambda_a}\Rightarrow \dfrac{1}{1.33}=\dfrac{\lambda_w}{589\times 10^{-9}}\Rightarrow \lambda_w=443\ nm$$

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

d) $$\dfrac{\mu_a}{\mu_w}=\dfrac{v_w}{v_a}\Rightarrow v_w=\dfrac{\mu_a v_a}{\mu_w}=\dfrac{3\times 10^8}{1.33}=2.25\times 10^8\ m/sec$$.

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