Question

Air has refractive index $1.0003$. The thickness of air column, which will have one more wavelength of yellow light $\left(6000\stackrel{\circ }{A}\right)$ then in the same thickness of vacuum is :

• A. $2mm$
• B. $2cm$
• C. $2m$
• D. $2km$

Answer 1

The correct option is A $2mm$

Given, Refractive index of vacuum, ${\mu }_v=1$ and Refractive index of air, ${\mu }_a=1.0003$

$\therefore \frac{{\lambda }_v}{{\lambda }_a}=\frac{{\mu }_a}{{\mu }_v}=1.0003$

$forvacuumt={\lambda }_1,forairt={\lambda }_a(n+1)$

$\frac{n+1}{n}=\frac{{\lambda }_v}{{\lambda }_a}=1.0003$

$1+\frac{1}{n}=1.0003\Rightarrow \frac{1}{n}=0.0003$

$n=\frac{1}{0.0003}=\frac{{10}^4}{3}\therefore t={\lambda }_{v}n$

$=6000\times {10}^{-10}\times \frac{{10}^4}{3}=2\times {10}^{-3}m=2mm$.