A slit of width 'a' is illuminated by red light of wavelength 6500 mathringA. If the first diffraction minimum falls at 30 mathringA, then the value of ' a ' is

Question

A slit of width 'a' is illuminated by red light of wavelength 6500 mathringA. If the first diffraction minimum falls at 30 mathringA, then the value of ' a ' is (A) 6.5 × 10-4 mm (B) 1.3 micron (C) 3250 mathringA (D) 2.6 × 10-4 cm

Tardigrade Admin · Accepted Answer

For diffraction minima a sin θ= n λ n =1 for I minimum a =(λ/ sin θ)=(6.5 × 10-7/ sin 30) =(6.5 × 10-7/0.5) =13 × 10-7 =1.3 × 10-6 m =1.3 micron

Q. A slit of width 'a' is illuminated by red light of wavelength $6500 \overset{˚}{A}$ . If the first diffraction minimum falls at $30 \overset{˚}{A}$ , then the value of ' $a$ ' is

$6.5 \times 1 0^{- 4} mm$

$1.3$ micron

$3250 \overset{˚}{A}$

$2.6 \times 1 0^{- 4} c m$

For diffraction minima
$a sin θ = nλ$
$n = 1$ for $I$ minimum
$a = \frac{λ}{s i n θ} = \frac{6.5 \times 1 0 ^{- 7}}{s i n 30}$
$= \frac{6.5 \times 1 0 ^{- 7}}{0.5}$
$= 13 \times 1 0^{- 7}$
$= 1.3 \times 1 0^{- 6} m$
$= 1.3$ micron

Q. A slit of width 'a' is illuminated by red light of wavelength 6500A˚. If the first diffraction minimum falls at 30A˚, then the value of ' a ' is

6.5×10−4mm

1.3 micron

3250A˚

2.6×10−4cm