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Wave Optics question

2004 · Shift 0 · Q119
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Wave Optics question

2004 · Shift 0 · Q119

JEE MainPhysicsWave OpticsMCQ+4 / −1
The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment, is :
  1. A
    three
  2. B
    five
  3. C
    infinite
  4. D
    zero
View written solutionFree

Correct answer: B

  1. Condition for interference maxima in YDSE

    In Young's double-slit experiment, bright fringes (maxima) occur when the path difference satisfies dsin⁡θ=nλd\sin\theta = n\lambdadsinθ=nλ where:

    • ddd = slit separation
    • λ\lambdaλ = wavelength
    • nnn = order of maximum (0,±1,±2,…0, \pm 1, \pm 2, \dots0,±1,±2,…)
  2. Given data

    The slit separation is twice the wavelength: d=2λd = 2\lambdad=2λ

    Substituting into the maxima condition: 2λsin⁡θ=nλ2\lambda \sin\theta = n\lambda2λsinθ=nλ 2sin⁡θ=n2\sin\theta = n2sinθ=n sin⁡θ=n2\sin\theta = \frac{n}{2}sinθ=2n​

  3. Possible values of nnn

    Since sin⁡θ\sin\thetasinθ must satisfy −1≤sin⁡θ≤1-1 \le \sin\theta \le 1−1≤sinθ≤1 we must have −1≤n2≤1-1 \le \frac{n}{2} \le 1−1≤2n​≤1 −2≤n≤2-2 \le n \le 2−2≤n≤2

    Thus the allowed integer values of nnn are: n=−2,−1,0,1,2n = -2, -1, 0, 1, 2n=−2,−1,0,1,2

  4. Count the maxima

    These correspond to:

    • second order on one side: n=−2n=-2n=−2
    • first order on one side: n=−1n=-1n=−1
    • central maximum: n=0n=0n=0
    • first order on the other side: n=1n=1n=1
    • second order on the other side: n=2n=2n=2

    So total number of possible maxima is 555

  5. Check options

    • A: three →\to→ incorrect
    • B: five →\to→ correct
    • C: infinite →\to→ incorrect
    • D: zero →\to→ incorrect

Final Answer: B: five\boxed{\text{B: five}}B: five​

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