A light wave is incident normally over a single slit of width 24 × 10-5 cm. The angular position of second dark fringe from the central maxima is 30°. What is the wavelength of light?

Question

A light wave is incident normally over a single slit of width 24 × 10-5 cm. The angular position of second dark fringe from the central maxima is 30°. What is the wavelength of light? (A) 6000 mathringA (B) 5000 mathringA (C) 3000 mathringA (D) 1500 mathringA

Tardigrade Admin · Accepted Answer

For nth dark fringe in single slit, a sinθ = nλ For second dark fringe, a sinθ = 2λ So, 24 × 10-5 × 10-2 × sin 30° = 2λ ∴ λ= 6 × 10-7 m = 6000 mathringA

Q. A light wave is incident normally over a single slit of width $24 \times 1 0^{- 5} c m$ . The angular position of second dark fringe from the central maxima is $3 0^{°}$ . What is the wavelength of light?

$6000 \overset{˚}{A}$

$5000 \overset{˚}{A}$

$3000 \overset{˚}{A}$

$1500 \overset{˚}{A}$

For $n^{t h}$ dark fringe in single slit, a $s in θ = nλ$
For second dark fringe, a $s in θ = 2 λ$
So, $24 \times 1 0^{- 5} \times 1 0^{- 2} \times s in 3 0^{°} = 2 λ$
$∴ λ = 6 \times 1 0^{- 7} m = 6000 \overset{˚}{A}$

Q. A light wave is incident normally over a single slit of width 24×10−5cm. The angular position of second dark fringe from the central maxima is 30°. What is the wavelength of light?

6000A˚

5000A˚

3000A˚

1500A˚