If wavelength `4500 Å` and `6000 Å` are found to be missing in the reflected spectrum in thin air film interference, the thickness of the film for normal incidence is nearly

Options

A. `9000 Å`
B. `10500 Å`
C. `5250 Å`
D. `4240 Å`

Answer

A

Explanation

For missing wavelength, use condition of minima
`2 mut-lambda/2=(2n+1)lambda/2`
`2 mut=(2n+1)lambda/2+lambda/2=(n+1)lambda`
For air `mu=1, t=(n+1)lambda/2`
`lambda=(2t)/(n+1)`
`n+1=(2t)/lambda_(1)`
`(n-1)+1=(2t)/lambda_(2)`
(i)-(ii)
`1=2t(1/lambda_(1)-1/lambda_(2))`
`=2t(1/4500-1/6000)=2t(1500/(4500xx6000))`
`t=9000 Å`