Figure shows two, identical narow slits `S_(1)` and `S_(2)`. A very small completely strip is placed at distacne `y` from the point `C`. `C` is the point on the screen equidistant from `S_(1)` and `S_(2)`. Assume `lamda lt lt d lt lt D`, where `lamda, d` and `D` have usual meaning. When `S_(2)` is covered the force due to light acting on strip is `f` and when both slits are opened the force acting on strip is `2f`. Find the minimum positive `y(lt lt D)` coordinate (in cm) of the strip if `(lamdaD)/d=4cm`

Answer

1

Explanation

Let `I_(0)` be the intensity at `P` due to individual slits `S_(1)` or `S_(2)`.
When waves due to both the sources superpose at `P`,the net intensity at `P` is `I=4I_(0)"cos"^(2) (piy)/(beta)`, where `beta=(lamdaD)/d`
Since force on strip at `P` is twice due to individual source
Hence `I=2I_(0)`
`:."cos"^(2) (piy)/2=1/2` or `(piy)/(beta)=(pi)/4` or `y=(beta)/4=(lamda D)/(4d)`