Refractive index of air is `1.0003.` The correct thickness of air column which will have one more wavelength of yellow light `(6000 Å)` than in the same thickness in vacuum is

Options

A. `2mm`
B. `2cm`
C. `2m`
D. `2km`

Answer

A

Explanation

Let x: number of wavelengths in vacuum
`(x+1)`: number of wavelengths in air
`x=(t)/(6000)` ….(i)
`x+1=(t)/((6000//1.0003))` …(ii)
(ii)-(i)
`1=(1.003-1)(t)/(6000)`
`t=(6000)/(0.003)Å=(6xx10^7)/(3)Å=2xx10^-3m=2mm`