In Young’s double-slit experiment net intensity of light at a point on screen is Inet = I1+I2+2√I1I2 cos ϕ
For I1 = I2 = I, Inet = 2I + 2I cos ϕ
Relation between path difference and phase difference is Δϕ =

2π

λ

Δx
For path difference λ, phase difference, Δϕ =

2π

λ

λ = 2π
Inet = K = 2I + 2I cos 2π or K = 4I ... (i)
For a path difference λ/3, phase difference
Δϕ =

2π

λ

Δx ⇒ ϕ =

2π

λ

(

λ

3

) =

2π

3

Now the intensity, Inet = 2I + 2I cos

2π

3

Inet = 2I - 2I sin 30° ⇒ Inet = I =

K

4