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 A

Options

A. 2 mm
B. 2 mm
C. 2 cm
D. 2.2 cm

Answer

B

Explanation

Difference in the number of wavelength = 1
If L is the thickness of air and vacuum columns then,
`L/lambda_(air) –L/lambda_(vaccum) =1`
`L(1/lambda_(air) –1/lambda_(vaccum)) =1`
`L(1/(lambda_(vaccum)/mu_(a)) –1/lambda_(vaccum)) =1`
`implies L/(lambda_(vaccume)) (mu_(a)-1)=1`
`implies L/(6000 xx 10^(-10)) (1.0003-1)=1`
` implies L=(6000xx10^(-10))/0.0003 = 2xx10^(-3)m=2mm`