Question

In Young's double slit experiment, the distance between two sources is $0.1 \,mm$. The distance of the screen from the source is $20\, cm$. Wavelength of light used is $5460\, ?$. The angular position of the first dark fringe is

• A. $0.08^{\circ}$
• B. $0.16^{\circ}$
• C. $0.20^{\circ}$
• D. $0.32^{\circ}$

Answer 1

Answer: (B)

$0.16^{\circ}$

Answer 2

For first dark fringe $x=\left(2n-1\right)\frac{\lambda}{2} \frac{D}{d}=\frac{\lambda}{2} \frac{D}{d} \left(\because\,n=1\right)$ Angular position, $\theta=\frac{x}{D}=\frac{\lambda}{2d}$ $=\frac{5460\times10^{-10}}{2\times10^{-4}}$ radian $=2730\times10^{-6}\times\frac{180}{\pi }$ degree $= 0.16^{\circ}$