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Wave Optics — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsWave Optics1 Mark
MCQ
Angular width of central maxima in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength $6000 \mathring A$. When the slit is illuminated by light of another wavelength, the angular width decreases by $30 \%$. The wavelength of this light will be
  • A
    $6000 \mathring A$
  • ✓
    $4200 \mathring A$
  • C
    $3000 \mathring A$
  • D
    $1800 \mathring A$
✓

Answer

Correct option: B.
$4200 \mathring A$
$\text { Angular width } \beta=\frac{2 \lambda}{d}$
$ \Rightarrow \beta \propto \lambda $
$\Rightarrow \frac{\beta_1}{\beta_2}=\frac{\lambda_1}{\lambda_2} $
$\Rightarrow \frac{\beta}{\frac{70}{100} \beta}=\frac{6000}{\lambda_2}$
$\Rightarrow \lambda_2=4200 \mathring A$

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