MCQ
In a $YDSE$ light of two different wavelengths ( $\lambda_1$ & $\lambda_2$) are incident normal to the plane of slits. The $n^{th}$ maxima of $\lambda_1$ coincides with the $m^{th}$ maxima of $\lambda_2$ exactly in front of one of the slits.

Given $D = \ 1.5\  m$
$d = 3\  mm$
$4500 \ Å < \lambda_1 , \lambda_2 < 7000\  Å$
then $n, m$ and $\lambda_1$ are

  • A
    $3,4,4000\ \mathop A\limits^0$
  • $5,6,6000\ \mathop A\limits^0$
  • C
    $2,3,5000\ \mathop A\limits^0$
  • D
    $4,5,3000\ \mathop A\limits^0 $

Answer

Correct option: B.
$5,6,6000\ \mathop A\limits^0$
b
${y_{{n^{th}}}} = \frac{{n{\lambda _1}D}}{{2d}};{\rm{n}} = 2,4,6,8 \ldots ..$

${y_{{m^{th}}}} = \frac{{m{\lambda _2}D}}{{2d}};{\rm{m}} = 2,4,6,8 \ldots  \ldots $

${y_{{n^{th}}}} = {y_{{m^{th}}}} = \frac{d}{2}$ from central fringe.

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