In an interfrence arrangement similar to Young's double- slit experiment, the slits S 1 & S 2 are illuminated with coherent microwave sources, each of frequency 10 6 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance d = 150.0 m and screen is at very large distance from slits. The intensity I( θ ) is measured as a function of θ , where θ is defined as shown. Screen is at a large distance. If I 0 is the maximum intensity then I ( θ ) for 0 ≤ θ ≤ 90º is given by:
for θ = 30º
for θ = 90º
Text Solution
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( a,c)
Sol. for θ = 30º; Δ P = d sin 30º = (150 m) × 
= 75 m.
⇒ Δφ = 75 × 
= 
= 
⇒ I res = I + I + 2 I cos ( Δφ ) = 2I
where I = 
{ maximum intensity = I 0 = 4 I } ⇒ I res = 
θ = 0º will automatically correspond to central maxima.
θ = 90º will correspond to path diff = d. = 150 m ⇒ Δφ = 
= π
⇒ minima
Hence intensity will be 0 at θ = 90º.
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