In a Youngs experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, the wavelength monochromatic light used would be

Question

In a Youngs experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, the wavelength monochromatic light used would be (A)  60× 10-4cm  (B)  10× 10-4cm  (C)  10× 10-5cm  (D)  6× 10-5cm

Tardigrade Admin · Accepted Answer

Distance of nth dark fringe from central fringe xn=((2 n-1) λ D/2 d) ∴ x2=((2 × 2-1) λ D/2 d) =(3 λ D/2 d) ⇒ 1 × 10-3=(3 λ × 1/2 × 0.9 × 10-3) ⇒ λ=6 × 10-5 cm

Q. In a Youngs experiment, two coherent sources are placed $0.90 mm$ apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of $1 mm$ from the central fringe, the wavelength monochromatic light used would be

$60 \times 1 0^{- 4} c m$

$10 \times 1 0^{- 4} c m$

$10 \times 1 0^{- 5} c m$

$6 \times 1 0^{- 5} c m$

Distance of nth dark fringe from central fringe
$x_{n} = \frac{( 2 n - 1 ) λ D}{2 d}$
$∴ x_{2} = \frac{( 2 \times 2 - 1 ) λ D}{2 d}$
$= \frac{3 λ D}{2 d}$
$\Rightarrow 1 \times 1 0^{- 3} = \frac{3 λ \times 1}{2 \times 0.9 \times 1 0 ^{- 3}}$
$\Rightarrow λ = 6 \times 1 0^{- 5} c m$

Q. In a Youngs experiment, two coherent sources are placed 0.90mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1mm from the central fringe, the wavelength monochromatic light used would be

60×10−4cm

10×10−4cm

10×10−5cm

6×10−5cm