The refractive index of air is 1.0003. The th | vedclass

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(A) Let the thickness of the column be $t$. In a vacuum,the number of wavelengths $n$ is given by $t = n \lambda_0$,where $\lambda_0 = 6000 \mathring

Vedclass · Accepted Answer

$2 \, mm$

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(A) Let the thickness of the column be $t$. In a vacuum,the number of wavelengths $n$ is given by $t = n \lambda_0$,where $\lambda_0 = 6000 \mathring A = 6 	imes 10^{-7} \, m$.In air,the wavelength is $\lambda_a = \frac{\lambda_0}{\mu}$,where $\mu = 1.0003$.The number of wavelengths in air for the same thickness $t$ is $(n+1)$,so $t = (n+1) \lambda_a$.Equating the two expressions for $t$: $n \lambda_0 = (n+1) \frac{\lambda_0}{\mu}$.Dividing by $\lambda_0$: $n = \frac{n+1}{\mu} \implies n\mu = n+1 \implies n(\mu - 1) = 1$.Thus,$n = \frac{1}{\mu - 1}$.Substituting $n$ into the first equation: $t = \frac{\lambda_0}{\mu - 1}$.$t = \frac{6 	imes 10^{-7}}{1.0003 - 1} = \frac{6 	imes 10^{-7}}{0.0003} = \frac{6 	imes 10^{-7}}{3 	imes 10^{-4}} = 2 	imes 10^{-3} \, m = 2 \, mm$.

The refractive index of air is $1.0003$. The thickness of an air column that will contain one more wavelength of yellow light $(6000 \mathring A)$ than in the same thickness in a vacuum is:

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