Question

A beam of light consisting of two wavelength $6300A^{\circ }$ and $\lambda A^{\circ }$ is used to obtain interference fringes in a Young’s double slit experiment. If $4^{th}$ bright fringe of $6300A^{\circ }$ coincides with $5^{th}$ dark fringe of $\lambda A^{\circ }$, the value of $\lambda \left(\text{in}{A}^{\circ }\right)$ is

• A. $5200$
• B. $4800$
• C. $6200$
• D. $5600$

Answer 1

The correct option is D $5600$

Given that $4^{th}\left(n_1\right)$ bright fringe coincides with $5^{th}\left(n_2\right)$ dark fringe
$\therefore \frac{n_1{\lambda }_{1}D}{d}=\frac{(2n_2-1){\lambda }_{2}D}{2d}$
$4\times 6300=\left(4.5\right)\lambda$
$\lambda =\frac{4\times 6300}{9}\times 2=5600A^{\circ }$