Explanation

(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
$V_{m}^{'} = \frac{\sigma}{\varepsilon_{0}}\left\{ \left( d + d^{'} \right) - t + \frac{t}{K} \right\}$ …(iii)
According to question $V_{air} = V_{m}'$ which gives $K = \frac{t}{t - d^{'}}$
Hence $K = \frac{2}{2 - 1.6} = 5$