In YDSE, the sources is red ligth of wavelength `7 xx 10^(-7) m`. When a thin glass plate of refractive index 1.5 is put in the path of one of the interfering beams, the central bright fringe shifts by `10^(-3)` m to the position previously occupied by the 5th bright fringe.
If the source is now changed to green light of wavelength `10^(-7)m`, the central fringe shifts to a position initially occupied by the sixth bright fringe due to red ligth. What will be refractive index of glass plate for the second ligth for changed source of ligth?

Answer

`7 mu m, 1.6, 0.57 xx 10^(-4) m`

Explanation

As due to presence of glass plate path difference changes by `(mu - 1) t` so according to givne problem
`(mu_(R) -1)t = 5 lambda_(R)`
`implies t = (5 xx 7 xx 10^(-7))/((1.5 - 1)) = 7 mu m`
Now, when red light is replaced by green light,
`(mu G - 1) t = 6 lambda_(R)`
So, `(mu_(R) - 1)/(mu_(G) - 1) = (5)/(6)`
`implies mu_(G) -1 = (6)/(5) (1.5 - 1)`
`mu_(G) = 1.6`
Further, as `5 beta_(R) = 10^(-3)`, i.e., `beta_(R) = 2 xx 10^(-4)`
`:. (beta_(G))/(beta_(R)) = (lambda_(G))/(lambda_(R)) = (5)/(7)`
`implies (beta_(G) - beta_(R))/(beta_(R)) = (5)/(7) - 1 = - (2)/(7)`
` implies Delta beta = - (2)/(7) xx 2 xx 10^(-4) = - 0.57 xx 10^(-4) m`
Hence, fringe width will decrease by `0.57 xx 10^(-4) ` m when red light is replaced by green light.