Question

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 }_a=$1.0003 ; Wavelength of yellow light in vacuum $=6000A^{\circ }$)

• A. $1.8mm$
• B. $2mm$
• C. $2cm$
• D. $2.2cm$

Answer 1

The correct option is B $2mm$

No of wavelengths $=\frac{thickness}{wavelength}$
Let $x$ be the thickness of the air column

so $\frac{x}{{\lambda }_{air}}-\frac{x}{{\lambda }_{vacuum}}=1$

$\frac{x}{\lambda }(1.0003-1)=1$

$x=\frac{6000\times {10}^{-10}}{0.0003}m$

$=2mm$