In the Young's double slit experiment, the intensity of light at a point on the screen where the path difference λ. is K, (λ. being the wavelength of light used). The intensity at a point where the path difference is λ/4 will be

Intensity at any point on the screen is I=4I0cos2ϕ2where I0 is the intensity of either wave and ϕ is the phase different between two waves. Phase difference, ϕ=2πλ×path differenceWhen path difference is λ, then ϕ=2πλ×λ=2π∴  I=4I0cos22π2=4I0cos2(π)=4I0=K                   . . . . .(i) When path difference is λ4, then ϕ=2πλ×λ4=π2∴  I=4I0cos2π4=2I0=K2