If amplitudes are a and 2a, I_max=(a+2a)^2=9a^2 and I_min=(2a-a)^2=a^2, so ratio is 9:1.

Maximum resultant amplitude is (a1+a2), so maximum intensity ∝ (a1 + a2)^2; the OCR shows this option selected.

Young's double-slit fringe spacing β = λL/d = (500×10^-9 m × 1 m)/(1×10^-3 m) = 5×10^-4 m = 0.5 mm.

Typical X-ray wavelengths are about 1 Å (10^-10 meter), so the order of 1 Å is the correct choice among the provided options.

For reflected bright fringes with one phase inversion, 2 n t = (m+1/2)λ; for n=1.4 and t=10000 Å, m=5,6,4 give λ ≈ 5091 Å, 4308 Å, 6222 Å (set ordered in option B).

Fringe width is proportional to wavelength, so new width = 1.0 mm × (6000/5000) = 1.2 mm.

Fringe width ∝ wavelength, so changing from blue to violet (shorter λ) decreases fringe width.

Coherence requires same wavelength and stable phase; differing intensities do not prevent coherence, so sources 3 and 4 can be coherent.

Spacing a = 1/N = 1/(5×10^5) m = 2×10^-6 m = 0.2×10^-3 cm, matching option A.

Diffraction angle scales with wavelength; increasing wavelength increases the diffraction angle for a given obstacle size.