Question

Find the angular separation between the consecutive bright fringes in a Young's double slit experiment with blue-green light of wavelength 500 nm. The separation between the slits is $2·0\times {10}^{-3}\mathrm{m}$.

Answer 1

Given:
Wavelength of the blue-green light, $\lambda =500\times {10}^{-9}\mathrm{m}$
Separation between two slits, $d=2\times {10}^{-3}\mathrm{m},$
Let angular separation between the consecutive bright fringes be θ.
$$\begin{gathered} \mathrm{Using}\theta =\frac{\mathit{}\beta }{D}=\frac{\lambda D}{dD}=\frac{\lambda }{d},\text{we get:} \\ \theta =\frac{500\times {10}^{-9}}{2\times {10}^{-3}} \\ =250\times {10}^{-6} \\ =25\times {10}^{-5}\mathrm{radian}\mathrm{or}0.014° \end{gathered}$$
Hence, the angular separation between the consecutive bright fringes is 0.014 degree.