A thin glass plate of thickness t and refractive index `mu` is inserted between screen and one of the slits in a young's experiment. If the intensity at the centre of the screen is I, what was the intensity at the same point prior to the introduction of the sheet.

Answer

(i) `I_(0)=Icos^(2)[(pi(mu-1)t)/(lamda)]`

Explanation

Due to the introduction of sheet in front of one slit (thickness t and refrective index `mu`) the shift
`=(D)/(d)(mu-1)t`
i.e., the path difference becomes `(mu-1)t` instead of zero at centre of screen `(Deltaxne0)`
`therefore ` Phase difference `=(2pi)/(lamda)xx(mu-1)t`
`therefore` Resultant intensity
`I_(0)=(I)/(4)+(I)/(4)+2sqrt((I)/(4))sqrt((I)/(4))cos[(2pi)/(lamda)(mu-1)t]`
Intensity at centre `I=4I'impliesI'=(I)/(4)`
`'I`- intensity due to one slit]
`I_(0)=(2I)/(4)[1+cos[(2pi)/(lamda)(mu-1)t]]`
`I_(0)=Icos^(2)[(2pi)/(lamda)((mu-1t))/(2)]=Icos^(2)((pi(mu-1)t)/(lamda))`