Physics · Interference: Young's double-slit experiment and expression for fringe width, coherent sources and sustained interference of light
Two monochromatic (wavelength and coherent source of electromagnetic waves are p
Two monochromatic (wavelength \( =\boldsymbol{a} / \mathbf{5} \) and coherent source of electromagnetic waves are placed on the \( x \) -axis at the point \( (2 a, 0) \) and \( (-a, 0) . \) A detector moves in a circle of radius \( R(>>2 a) \) whose Centre is at the origin. The number of maximas detected during one circular revolution by the detector are:
- A. 60
- B. 15
- C. 64
- D. None
Step-by-step solution
Source separation d = 3a, wavelength λ = a/5. For a distant detector on circle of radius R >> 2a, path difference ≈ d|cosθ|. Maxima occur when d|cosθ| = nλ, so 3a|cosθ| = n(a/5) ⇒ |cosθ| = n/15. n integer, 0 ≤ n ≤ 15. For n=0 and n=15, |cosθ| = 0 or 1 giving 2 angles each. For 1 ≤ n ≤ 14, |cosθ| is strictly between 0 and 1, giving 4 angles each (since cosθ = ±n/15). Total maxima = 2 (n=0) + 14×4 + 2 (n=15) = 60.
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