In Young's double-slit experiment using monochromatic light of wavelength `lambda`, the intensity of light at a point on the screen where path difference is `lambda`, is K units. What is the intensity of light at a point where path difference is `lambda//3`?

Explanation

In YDSE (Young.s Double Slit Experiment), intensity of light at a given point on the screen is,
`I=I_(0)cos^(2){(k(r_(2)-r_(1)))/(2)}`
For first point, `r_(2)-r_(1)=lamda` I=K and so,
`K=I_(0)cos^(2){(1)/(2)xx(2pi)/(lamda)xxlamda}`
`:.K=I_(0)(1)`
`:.I_(0)=K" "....(1)`
For second point, `(r_(2)-r_(1))=(lamda)/(3)` and so,
`I.=I_(0)cos^(2){(k(r_(2)-r_(1)))/(2)}`
`:.I.=Kcos^(2){(1)/(2)xx(2pi)/(lamda)xx(lamda)/(3)}`
`:.I.=Kcos^(2)((pi)/(3))=K((1)/(2))^(2)`
`:.I.=(K)/(4)`