Angular width of central maxima in the Fraunhoffer diffraction pa… - Vidyadip

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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