In a arrangement of Young experiment the central fringe of interference pattern produced by light of wavelength 6000 Å so the central fringe is superposing to 4th order dark fringe, after a glass plate of refractive index 1.5 is introduced. The thickness of the glass plate would be ......

Options

A. `6xx10^(-6)m`
B. `4.5xx10^(-6)m`
C. `4.2xx10^(-6)m`
D. `4.8xx10^(-6)m`

Answer

C

Explanation

Thickness of plate `t=(xd)/(D(mu-1)) " "...(1)`
but `(xd)/(D)=(2n-1)(lambda)/(2)`
`(xd)/(D)=(7lambda)/(2) " "...(2) n=4` dark
`:.` From equation (1) and (2),
`t=(7lambda)/(2(mu-1))`
`=(7xx6xx10^(-7))/(2(1.5-1.0))=(21xx10^(-7))/(0.5)=4.2xx10^(-6)m`