The difference in the number of wavelengths, when yellow light propagates through air and vacuum columns of…
The difference in the number of wavelengths, when yellow light propagates through air and vacuum columns of the same thickness, is one. The thickness of the air column is Refractive index of air $\mu_c=1.0003$, Wavelength of yellow light in vacuum $=6000 Ã…$
$1.8 \mathrm{~mm}$
$2 \mathrm{~mm}$
$2 \mathrm{~cm}$
$2.2 \mathrm{~cm}$
Solution
Difference in the number of wavelength $=1$. If ' $L$ ' is the thickness of air and vacuum columns.
$\begin{aligned} & \frac{L}{\lambda_{\text {st }}}-\frac{L}{\lambda_{\text {man }}}=1 \\ & L\left(\frac{1}{\lambda_m}-\frac{1}{\lambda_{n m}}\right)=1 \\ & L\left(\frac{1}{\frac{\lambda_{\mathrm{m}=}}{\mu_{\mathrm{m}}}}-\frac{1}{\lambda_{\mathrm{van}}}\right)=1 \\ & L\left(\frac{\mu_{-}}{\lambda_{\operatorname{man}}}-\frac{1}{\lambda_{\operatorname{man}}}\right)=1 \\ & \frac{L}{\lambda_{\text {eme }}}\left(\mu_{\mathrm{N}}-1\right)=1 \\ & \frac{L}{6000 \times 10^{-10}}(1.0003-1)=1 \\ & L=\frac{6000 \times 10^{-20}}{0.0003}=\frac{6 \times 10^{-7}}{3 \times 10^{-4}} \\ & =2 \times 10^{-2} \mathrm{~m}=2 \mathrm{~mm} \\ & \end{aligned}$