Q. In a Young’s 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 of monochromatic light used would be
A) $60 \times 10^{- 4}cm$
B) $10 \times 10^{- 4}cm$
C) $10 \times 10^{- 5}cm$
D) $6 \times 10^{- 5}cm$
Explanation
(d) Distance of $n^{th}$ dark fringe from central fringe
$x_{n} = \frac{(2n - 1)\lambda D}{2d}$
$\therefore x_{2} = \frac{(2 \times 2 - 1)\lambda D}{2d} = \frac{3\lambda D}{2d}$
$\Rightarrow 1 \times 10^{- 3} = \frac{3 \times \lambda \times 1}{2 \times 0.9 \times 10^{- 3}} \Rightarrow \lambda = 6 \times 10^{- 5}cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.