Q. In Young’s double slit experiment the intensity of light at a point on the screen where the path difference is λ is K. The intensity of light at a point where the path difference is λ /3 [ λ is the wavelength of light used] is

(a) K/4

(b) K/3

(c) K/2

(d) K

Ans:(a)

Sol: I_{R} = I+I+2√(I.I)cosφ

I_{R} = 2I(1+cosφ ) = 2I.2cos^{2}(φ/2) = 4Icos^{2}(φ/2)

A/c to question , K = 4Icos^{2 }π (As path diff. is λ hence phase diff. is 2π)

K = 4I …….(i)

In 2nd case , I_{R}‘ = 4Icos^{2}(φ’/2)

I_{R}‘ = 4Icos^{2}(2π/3×2) (As path diff. is λ/3 hence phase diff. is 2π/3)

= 4Icos^{2}(π/3) = 4I×1/4 = I = K/4 from (i)