Q139 / 180 · COMEDK 2016 · Physics

In Young's double slit experiment, 1st dark fringe occurs directly opposite to a slit. Wavelength of light used is

  • Correct answer
    A
    $d^{2} / D$
  • B
    $d / D$
  • C
    $D^{2} / d$
  • D
    $2 d^{2} / D$

Solution

For dark fringe, path difference, $\Lambda x=\left(n+\frac{1}{2}\right) \lambda$ Also, $\quad \Delta x=\frac{d y}{D} \Rightarrow \frac{d y}{D}=\left(n+\frac{1}{2}\right) \lambda$ For 1st dark fringe at directly opposite point of slit $n=0, y=\frac{d}{2}$ $\Rightarrow \quad \frac{d\left(\frac{d}{2}\right)}{D}=\frac{\lambda}{2} \Rightarrow \lambda=\frac{d^{2}}{D}$

Hence, the correct answer is option: 'A'.

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