a
(a) In air the potential difference between the plates
\({V_{air}} = \frac{\sigma }{{{\varepsilon _0}}}.d\) ..... \((i)\)
In the presence of partially filled medium potential difference between the plates
\({V_m} = \frac{\sigma }{{{\varepsilon _0}}}(d - t + \frac{t}{K})\) ..... \((ii)\)
Potential difference between the plates with dielectric medium and increased distance is
\({V_m}' = \frac{\sigma }{{{\varepsilon _0}}}\left\{ {(d + d') - t + \frac{t}{K}} \right\}\) ..... \((iii)\)
According to question \({V_{air}} = {V_m}'\) which gives \(K = \frac{t}{{t - d'}}\)
Hence \(K = \frac{2}{{2 - 1.6}} = 5\)