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  4. 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 mathringA ]

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Q. 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 $=6000 \,\mathring{A}$ ]

JEE MainJEE Main 2021Wave Optics

Solution:

Thickness $t=n \lambda$
So, $n \lambda_{\text {vac }}=(n+1) \lambda_{\text {air }}$
$n \lambda=(n+1) \frac{\lambda}{\mu_{\text{ air }}}$
$n=\frac{1}{\mu_{\text {air }}-1}=\frac{10^{4}}{3}$
$t =n \lambda $
$=\frac{10^{4}}{3} \times 6000\,\mathring{A}$
$=2\, mm$