In Young's double slit experiment, the intensity at a point is (1 /4) of the maximum intensity. The angular position of this point is

Let P be the point at angular position θ where the intensity is (1 /4 ) of &e maximum intensity as shown in fig. (a). We know that  I=Imaxcos2⁡ϕ2 Imax4=Imaxcos2⁡ϕ2  or  4cos2⁡ϕ2=1 cos2⁡ϕ2=14  or  cos⁡ϕ2=12 ϕ2=cos−1⁡12=60∘  or  ϕ=120∘=2π3 2πλ×dsin⁡θ=2π3  or  θ=sin−1⁡λ3d