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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Wave Optics

NTA Abhyas 2020 · Physics · Wave Optics

In Young's double slit experiment, how many maxima can be obtained...

In Young's double slit experiment, how many maxima can be obtained on a screen (including central maxima), if d=5λ2\text{d} = \dfrac{5 \lambda}{2 } (where λ\lambda is the wavelength of light)?

Options

  1. A5\text{5}
  2. B4\text{4}
  3. C7\text{7}
  4. D1\text{1}

Correct answer

A. 5\text{5}

Step-by-step solution

In YDSE, path difference, Δx=d sinθ\Delta \text{x} = \text{d sin} \theta

For maxima, Δx=nλ\Delta \text{x} = \text{n} \lambda, where n=0,±1,±2....\text{n} = 0 \text{,} \pm 1 \text{,} \pm 2 \text{....}

\dfrac{5 \lambda}{2} \text\sin \theta = \text{n} \lambda (given that d=5λ2\text{d} = \dfrac{5 \lambda}{2})

⇒sinθ=2n5.........(i)\begin{array}{ll}⇒ sin\theta = \dfrac{2n}{5} ......... ( i )\end{array}

Since,−1≤sinθ≤1- 1 \le sin\theta \le 1 Form (i)⇒−1≤2n/5≤1⇒ - 1 \le 2n / 5 \le 1

So, −52≤n≤52- \dfrac{5}{2} \le \text{n} \le \dfrac{5}{2}

So, possible values of n are -2, -1, 0, 1, 2\text{-2, -1, 0, 1, 2}. Thus a total of 5\text{5} maxima will be obtained.
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