The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one.

Question:

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is ______ mm. [Refractive index of air = 1.0003, wavelength of yellow light in vacuum = 6000 Å]

Solution:

Thickness $\mathrm{t}=\mathrm{n} \lambda$

So, $\mathrm{n} \lambda_{\mathrm{vac}}=(\mathrm{n}+1) \lambda_{\mathrm{air}}$

$\mathrm{n} \lambda=(\mathrm{n}+1) \frac{\lambda}{\mu_{\mathrm{air}}}$

$\mathrm{n}=\frac{1}{\mu_{\mathrm{air}}-1}=\frac{10^{4}}{3}$

$\mathrm{t}=\mathrm{n} \lambda$

$=\frac{10^{4}}{3} \times 6000 A$

$=2 \mathrm{~mm}$

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