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\times 10^{-4}cm $
• B. $ 10\times 10^{-4}cm $
• C. $ 10\times 10^{-5}cm $
• D. $ 6\times 10^{-5}cm $

Answer 1

Answer: (D)

Distance of nth dark fringe from central fringe
$x_{n}=\frac{(2 n-1) \lambda D}{2 d} $
$\therefore x_{2}=\frac{(2 \times 2-1) \lambda D}{2 d}$
$=\frac{3 \lambda D}{2 d}$
$ \Rightarrow 1 \times 10^{-3}=\frac{3 \lambda \times 1}{2 \times 0.9 \times 10^{-3}}$
$ \Rightarrow \lambda=6 \times 10^{-5}\, cm$