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 = 6000 `overset(circ)(A)`)

Options

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

Answer

b

Explanation

Difference in number of wave lengths = 1
If `t` is the thickness of air and vacuum columns then,
`implies t/lambda_(u) –t/lambda_(v)=1`
`t(1/lambda_(u) –1/lambda_(v))=1`
`implies t(1/(lambda_(v)/lambda_(u)) –1/lambda_(v))=1`
`impliest/lambda_(v) [mu_(u)-1]=1impliest=lambda_(v)/(mu_(u)-1)`
`implies t=(6000xx10^_(10))/(1.0003-1)`