the intensity at the central maxima (o) in a young's double slit experiment is Io If the distance OP - Physics - Wave Optics

Question

the intensity at the central maxima (o) in a young's double slit
experiment is Io If the distance OP equals 1/3rd of the
fringe width of the pattern , show that the intensity at a point
would be I0/4
in the experiment on diffraction due to single slit show that
I) The intensity of diffraction fringes decreases as the order n
increases
ii) angular width of the central maximum is twice that of the firdt
order secondary maximum

Hansraj Rai · Accepted Answer

Phase difference is zero at point O Intensity at point O is, $I_{0} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos θ I_{1} = I_{2} I_{0} = I + I + 2 \sqrt{I \times I} \cos 0 I_{0} = 4 I (i)$ Path difference at point P is, x = Î»/3 Phase diffidence, $φ = \frac{2 π}{3}$ $I_{P} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos φ I_{1} = I_{2} I_{P} = I + I + 2 \sqrt{I \times I} \cos 120 I_{P} = I + I - 2 \sqrt{I \times I} \cos 120 I_{P} = 2 I - I = I f r o m (i), I_{P} = \frac{I_{0}}{4}$ For the last part please refer to the study material