In Young's double slit experiment, white light is used. The separation between the slits is b. The screen is at a distance d (d>> b) from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are

Path difference between the rays reaching infront of slit S1 is.S1P−S2P=b2+d21/2−dFor distructive interference at P S1P-S2P=(2 n-1)λ2i.e (b2+d2)1/2-d=(2n-1)λ2⇒d 1+b2d21/2-d=(2n-1)λ2⇒d 1+b22d2+......-d=(2n-1)λ2(Binomial Expansion) ⇒b2d=(2n-1)λ2⇒λ=b2(2n-1)dFor n=1, 2............, λ=b2d, b23d