Q143 / 160 · AP EAMCET 2022 (06 Jul Shift 1) · Physics

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

  • A
    $7.5 \mu \mathrm{m}$
  • Correct answer
    B
    $0.75 \mu \mathrm{m}$
  • C
    $0.075 \mu \mathrm{m}$
  • D
    $75 \mu \mathrm{m}$

Solution

For second order dark fringe $$ \Delta \mathrm{x}=\frac{3 \lambda}{2} \quad\left[\because \Delta \mathrm{x}=\left(\mathrm{n}-\frac{1}{2}\right) \lambda, \text { for } n \text {th minima }\right] $$ $\begin{aligned} & \Rightarrow \mathrm{O}_1 \mathrm{R} \sim \mathrm{O}_2 \mathrm{R}=\frac{3}{2} \times 5000=7500 Å \\ & =0.75 \mu \mathrm{m}\end{aligned}$

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

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