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

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

\( \text{(a) } 60 \times 10^{-4}\ \text{cm} \)

\( \text{(b) } 10 \times 10^{-4}\ \text{cm} \)

\( \text{(c) } 10 \times 10^{-5}\ \text{cm} \)

\( \text{(d) } 6 \times 10^{-5}\ \text{cm} \)

Answer :  \( \text{(d) } 6 \times 10^{-5}\ \text{cm} \)

\(\text{Maxima: } x_n = n \frac{\lambda D}{d}\)  

\(\text{Minima: } x_n = (2n-1)\frac{\lambda}{2}\frac{D}{d}\)  

\(= \frac{3}{2}\lambda \frac{D}{d}\)  

\(1 \times 10^{-3} = \frac{3}{2}\lambda \frac{1}{0.9 \times 10^{-3}}\)  

\(\lambda = \frac{2}{3} \times 0.9 \times 10^{-6}\)  

\(= 0.6 \times 10^{-6}\)  

\(= 6 \times 10^{-7}\)  

\(6 \times 10^{-7}\ \text{m}\)  

\(6 \times 10^{-7} \times 100\ \text{cm}\)  

\(= 6 \times 10^{-5}\ \text{cm}\)