In a Young’s double slit experiment a monochromatic light whose wavelength is l strikes on the slits, separated by distance d, as shown in the figure. Refractive index of the medium between slits and screen varies with time t as n = n0 + kt. Here n0 and k are positive constants. Position of any point P on screen is measure by its y-coordinate as shown.

If a glass plate of small thickness b is placed in front of S1. How should its refractive index vary with time so that central maxima is formed at O.

Explanation

(`a`) `S_(1)P-S_(2)P=(dy)/(D)`
`Deltax=(n_(0)+kt)(dy)/(D)-dsinphi=0`
For central maxima.
`:. y =(Dsinphi)/(n_(0)+kt)y`-coordinates of central maximum
(b) `(dy)/(dt)=(-kDsinphi)/((n_(0)+kt)^(2))=` velocity of central maximum
(`c`) For central maxima to be formed at `O`
`n'((n)/(n')-1)P=dsinphi` Here `n'=n_(0)+kt`, `n=` refractive index of plate
`n=n_(0)+kt+(dsinphi)/(P)`