Question

In a Young's double slit experiment, two narrow vertical slits placed 0⋅800 mm apart are illuminated by the same source of yellow light of wavelength 589 nm. How far are the adjacent bright bands in the interference pattern observed on a screen 2⋅00 m away?

Answer 1

Given:
Separation between two narrow slits, $d=0.8\mathrm{mm}=0.8\times {10}^{-3}\mathrm{m}$
Wavelength of the yellow light, $\lambda =589\mathrm{nm}=589\times {10}^{-9}\mathrm{m}$
Distance between screen and slit, $D=2.0\mathrm{m}$
Separation between the adjacent bright bands = width of one dark fringe
That is, $\beta =\frac{\lambda D}{d}$ ...(i)
$$\begin{gathered} \Rightarrow \beta =\frac{589\times {10}^{-9}\times 2}{0.8\times {10}^{-3}} \\ =1.47\times {10}^{-3}\mathrm{m} \\ =1.47\mathrm{mm}. \end{gathered}$$

Hence, the adjacent bright bands in the interference pattern are 1.47 mm apart.