A light source, which emits two wavelengths λ₁= 400 nm and λ₂ = 600 nm, is used in a Young's double slit experiment. If recorded fringe widths for λ₁ and λ₂​ are β₁ and β₂​ and the number of fringes for them within a distance y on one side of the central maximum are m₁ and m₂​, respectively, then

Fringe width $\beta =\frac{\lambda D}{d}$

$\Rightarrow \beta \propto \lambda$

Since, ${\lambda }_2>{\lambda }_1$

$\Rightarrow {\beta }_2>{\beta }_1$

Number of fringes in a given width

$$\begin{gathered} m=\frac{y}{\beta } \\ \Rightarrow m\propto \frac{1}{\beta } \end{gathered}$$

$\Rightarrow m_2<m_1$ as ${\beta }_2>{\beta }_1$

Distance of 3rd maximum (third bright) of ${\lambda }_2$ from central maximum

$y_{3B}=\frac{3{\lambda }_{2}D}{d}=\frac{1800D}{d}$

Distance of 5th minimum (fifth dark) of ${\lambda }_1$ from central maximum

$y_{5B}=\frac{9{\lambda }_{1}D}{2d}=\frac{1800D}{d}$

So, 3rd maximum of ${\lambda }_2$ will overlap with 5th minimum of ${\lambda }_1$.

Angular separation (or angular fringe width)$=\frac{\lambda }{d}\propto \lambda$

Angular separation for ${\lambda }_1$ will be lesser.