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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
Two coherent sources separated by distance d are radiating in phase having wavelength $\lambda$. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of $n = 4$ interference maxima is given as
  • A
    ${\sin ^{ - 1}}\frac{{n\lambda }}{d}$
  • ✓
    ${\cos ^{ - 1}}\frac{{4\lambda }}{d}$
  • C
    ${\tan ^{ - 1}}\frac{d}{{4\lambda }}$
  • D
    ${\cos ^{ - 1}}\frac{\lambda }{{4d}}$
✓

Answer

Correct option: B.
${\cos ^{ - 1}}\frac{{4\lambda }}{d}$
b
(b) Here path difference at a point $P$ on the circle is given by
$\Delta x = d\cos \theta $ ….. (i)
For maxima at $P$
$\Delta x = n\lambda $ ….. (ii)
From equation (i) and (ii)
$n\lambda = d\cos \theta \Rightarrow \theta {\cos ^{ - 1}}\left( {\frac{{n\lambda }}{d}} \right) = {\cos ^{ - 1}}\left( {\frac{{4\lambda }}{d}} \right)$

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