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Two coherent sources $\mathrm{O}_1$ and $\mathrm{O}_2$ in Young's double slit experiment are illuminated with monochromatic light of wavelength $5000 Å$. If a second order dark fringe is formed at a point $\mathrm{R}$ on the screen, the path difference $\mathrm{O}_1 \mathrm{R} \sim \mathrm{O}_2 \mathrm{R}$ is
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The correct answer is:
$0.75 \mu \mathrm{m}$
For second order dark fringe
$$
\Delta \mathrm{x}=\frac{3 \lambda}{2} \quad\left[\because \Delta \mathrm{x}=\left(\mathrm{n}-\frac{1}{2}\right) \lambda, \text { for } n \text {th minima }\right]
$$
$\begin{aligned} & \Rightarrow \mathrm{O}_1 \mathrm{R} \sim \mathrm{O}_2 \mathrm{R}=\frac{3}{2} \times 5000=7500 Å \\ & =0.75 \mu \mathrm{m}\end{aligned}$
$$
\Delta \mathrm{x}=\frac{3 \lambda}{2} \quad\left[\because \Delta \mathrm{x}=\left(\mathrm{n}-\frac{1}{2}\right) \lambda, \text { for } n \text {th minima }\right]
$$
$\begin{aligned} & \Rightarrow \mathrm{O}_1 \mathrm{R} \sim \mathrm{O}_2 \mathrm{R}=\frac{3}{2} \times 5000=7500 Å \\ & =0.75 \mu \mathrm{m}\end{aligned}$
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