MCQ
Two wavelengths of light $\lambda  _1$ and  $\lambda _2$ are sent through a young's double slit experiment simultaneously. If the third order bright fringe of $\lambda _1$ coincides with the fourth order bright fringe of $\lambda _2,$ then
  • $\frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{4}{3}$
  • B
    $\frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{3}{4}$
  • C
    $\frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{5}{4}$
  • D
    $\frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{4}{5}$

Answer

Correct option: A.
$\frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{4}{3}$
a
$\beta_{1}=\lambda_{1} \frac{D}{d}$

position for third order bright fringe, $y_{1}=3 \beta_{1}=3 \lambda_{1} \frac{D}{d}$

$\beta_{2}=\lambda_{2} \frac{D}{d}$

position for third order bright fringe, $y_{2}=4 \beta_{2}=3 \lambda_{2} \frac{D}{d}$

since $y_{1}=y_{2}$

$3 \lambda_{1} \frac{D}{d}=4 \lambda_{2} \frac{D}{d}$

$\Rightarrow \frac{\lambda_{1}}{\lambda_{2}}=\frac{4}{3}$

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