Air has refractive index `1.0003`. The thickness of air column, which will have one more wavelength of yellow light `(6000Å)` than in the same thickness of vaccuum is

Options

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

Answer

B

Explanation

We have, `mu_(v)=1 and mu_(a)=1.003`
`therefore (lambda_(v))/(lambda_(a))=(mu_(a))/(mu_(v))=1.003`
Now thickness of air column
`x=lambda_(v)n=lambda_(a)(n+1)`
`rArr (n+1)/(n)=(lambda_(v))/(lambda_(a))=1.003`
`rArr 1+(1)/(n)=1.003 or (1)/(n)=0.003`
`rArr n=(1)/(0.003)=(10^(3))/(3)`
`therefore x=lambda_(a)n=6000xx10^(-7)mm xx (10^(3))/(3)`
`=2xx10 mm = 2 cm `