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

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 - 10. Wave optics4 Marks
MCQ
In a single slit diffraction experiment first minimum for red light ($ \gamma =  660\, nm$) coincides with first maximum of some other wavelength $\lambda$'. The value of $\lambda$' is......$\mathop A\limits^o $
  • ✓
    $4400 $
  • B
    $6600 $
  • C
    $2000$
  • D
    $3500$
✓

Answer

Correct option: A.
$4400 $
a
(a)In a single slit diffraction experiment, position of minima is given by $d\sin \theta = n\lambda $
So for first minima of red $\sin \theta = 1 \times \left( {\frac{{{\lambda _R}}}{d}} \right)$
and as first maxima is midway between first and second minima, for wavelength $\lambda '$,
its position will be
$d\sin \theta ' = \frac{{\lambda ' + 2\lambda '}}{2} \Rightarrow \sin \theta ' = \frac{{3\lambda '}}{{2d}}$
According to given condition $\sin \theta = \sin \theta '$
$ \Rightarrow \lambda ' = \frac{2}{3}{\lambda _R}$ so $\lambda ' = \frac{2}{3} \times 6600 = 440\,nm$$ = 4400\,{Å}$

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