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STD 12 - 10. Wave optics — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 10. Wave optics4 Marks
MCQ
Using Young's double slit experiment, a monochromatic light of wavelength $5000\,\mathring A$ produces fringes of fringe width $0.5 \,mm$. If another monochromatic light of wavelength $6000\,\mathring A$ is used and the separation between the slits is doubled, then the new fringe width will be ............... $mm$
  • A
    $0.5$
  • B
    $1.0$
  • C
    $0.6$
  • ✓
    $0.3$
✓

Answer

Correct option: D.
$0.3$
d
Fringe width $\beta=\frac{ D \lambda}{ d }$

$\lambda_{1}=5000 \,\mathring A$

$\beta_{1}=\frac{ D }{ d }\left(5000 \times 10^{-10}\right)=5 \times 10^{-4} \,m$......$(I)$

$\beta_{2}=\frac{ D }{(2 d )}\left(6000 \times 10^{-10}\right)= x \text { (let) }$.....$(II)$

Divide $(II)$ and $(I)$

$\frac{\beta_{2}}{\beta_{1}}=\frac{3000 \times 10^{-10}}{5000 \times 10^{-10}}=\frac{x}{5 \times 10^{-4}}$

$x=3 \times 10^{-4} m \text { or } 0.3 \,mm$

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