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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
A slit of width $a$ is illuminated by white light. For red light ($\lambda = 6500 \;\mathring A$), the first minima is obtained at $\theta = {30^o}$. Then the value of $a$ will be
  • A
    $3250 Å$
  • B
    $6.5 \times {10^{ - 4}}mm$
  • ✓
    $1.24\; microns$
  • D
    $2.6 \times {10^{ - 4}}cm$
✓

Answer

Correct option: C.
$1.24\; microns$
c
(c)For first minima $\theta = \frac{\lambda }{a}$ or $a = \frac{\lambda }{\theta }$

$\therefore a = \frac{{6500 \times {{10}^{ - 8}} \times 6}}{\pi }$ (As $30°$  = $\frac{\pi }{6}$radian)

$ = 1.24 \times {10^{ - 4}}cm = 1.24$microns

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