Red light of wavelength 5400 A from a distant source falls on a s… - Vidyadip

MCQ

Red light of wavelength $5400$ $\mathring {A}$ from a distant source falls on a slit $0.80\, mm$ wide. Calculate the distance between first two dark bands on each side of central bright band in the diffraction pattern observed on a screen place $1.4\, m$ from the slit. (in $mm$)

✓
$1.89$
B
$4$
C
$1$
D
$3$

✓

Answer

Correct option: A.

$1.89$

a
Here wavelength $(\lambda)=5400 \dot{A}=5.4 \times 10^{-7} m , a=0.80 mm =8 \times 10^{-4} m , D=1.4 m$

$\therefore$ Distance between first two dark bands on each side of central maximum is the width of central maximum

$=2 x=\frac{2 \lambda D}{d}$

$=\frac{2 \times 5.4 \times 10^{-7} \times 1.4}{8 \times 10^{-4}}$

$=1.89 \times 10^{-3} m =1.89 mm$

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