A monochromatic light source of wavelength `lamda` is placed at S. three slits `S_(1),S_(2)` and `S_(3)` are equidistant from the source S and the point P on the screen `S_(1)P-S_(2)P=lamda//6` and `S_(1)P-S_(3)P=2lamda//3`. if I be the intensity at P when only one slit is open the intensity at P when all the three `slits` are open is-

Options

A. 3I
B. 5I
C. 8I
D. zero

Answer

A

Explanation

`d_(12)=(2pi)/(lamda)xx(lamda)/(6)xx2=(2pi)/(3)`
`d_(23)=(2pi)/(lamda)xx(lamda)/(2)xx2=2pi`
`A'=sqrt(((sqrt(3))/(2))^(2)+((3A)/(2))^(2))=sqrt(3)A`
`impliesIpropA^(2)impliesA_(R)^(2)=3A^(2)impliesI_(R)=3I`