Correct Answer - Option 3 : Both 1 and 2
CONCEPT:
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Interference: The combination of two or more electromagnetic waveforms to form a resultant wave that may have greater, lower, or the same amplitude is called interference.
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Constructive interference: When the resultant amplitude of the two interfering waves is maximum or equal to the sum of the individual amplitudes.
- For constructive interference, the superimposing waves must be in phase or the interfering wave must have the phase difference in the integer multiple of 2π.
The amplitude of the resultant wave is given by:
\(A=\sqrt{A_1^2+A_2^2+2A_1A_2cosϕ}\)
where A1 is the amplitude of the first wave, A2 is the amplitude of the second wave, and ϕ is the phase difference between both the waves.
CALCULATION:
- Given that- interference is constructive interference.
- Let the amplitude of the interfering waves is A1 and A2
- If the interference is constructive interference, the amplitude of the resultant wave (maximum) = A1 + A2
The amplitude of the resultant wave \(=\sqrt{A_1^2+A_2^2+2A_1A_2cosϕ}\)
\(A_1+A_2=\sqrt{A_1^2+A_2^2+2A_1A_2cosϕ}\)
\((A_1+A_2)^2={A_1^2+A_2^2+2A_1A_2cosϕ}\)
\({A_1^2+A_2^2+2A_1A_2}={A_1^2+A_2^2+2A_1A_2cosϕ}\)
1 = cos ϕ
ϕ = 0 or 2π or 4π .......
- So the correct answer is option 3.
- The phase difference for destructive interference is (2n + 1)π/2 i.e. π, 3π, 5π ............
