Question

In a Young's double slit experiment, two wavelengths of $500nm$ and $700nm$ were used. What is the minimum distance from the central maximum where their maximas coincide again? (Take $D/d={10}^3$ Symbols have their usual meanings.)

Answer 1

Let the $m^{th}$ maxima of $500nm$ wavelength coincides with the $n^{th}$ maxima of $700nm$ wavelength.

So, $Y_n=Y_m$

Or $\frac{n{\lambda }_{1}D}{d}=\frac{m{\lambda }_{2}D}{d}$

Or $n{\lambda }_1=m{\lambda }_2$

Or $n\times 700=m\times 500$

So, we get $n=5$ and $m=7$

So, minimum distance $Y_n=\frac{n{\lambda }_{1}D}{d}=5\times 700\times {10}^{-9}\times {10}^3=3.5\times {10}^{-3}m=3.5mm$