Option 1 (Atoms):
Step 1: Read the absorbed photon as an upward transition from the ground level \(n_i = 1\) to a higher level \(n_f = n\). The photon energy equals the energy gap: \(E_{photon} = 13.6\left(\dfrac{1}{n_i^2} - \dfrac{1}{n_f^2}\right)\) eV.
Step 2: Substitute: \(12.09 = 13.6\left(1 - \dfrac{1}{n^2}\right)\).
Step 3: \(1 - \dfrac{1}{n^2} = \dfrac{12.09}{13.6} = 0.889\), so \(\dfrac{1}{n^2} = 0.111\).
Step 4: \(n^2 = \dfrac{1}{0.111} = 9.0 \Rightarrow n = 3\). The highest reachable level is the third one.
\[\boxed{n = 3}\]
Option 2 (Interference):
Step 1: When two coherent waves \(y_1 = a\sin\omega t\) and \(y_2 = a\sin(\omega t + \phi)\) meet, their amplitudes combine to give a resultant amplitude \(R = 2a\cos(\phi/2)\), and the intensity follows \(I \propto R^2\).
Step 2: Maximum intensity (constructive) needs \(\cos(\phi/2) = \pm 1\), i.e. phase difference \(\phi = 2n\pi\), which is a path difference of \(n\lambda\).
Step 3: Minimum intensity (destructive) needs \(\cos(\phi/2) = 0\), i.e. \(\phi = (2n-1)\pi\), which is a path difference of \((2n-1)\lambda/2\).
\[\boxed{\text{Bright: path diff } n\lambda;\ \text{Dark: path diff } (2n-1)\lambda/2}\]