To solve this problem, we need to understand the relationship between the turns ratio and the voltage ratio in an ideal transformer.$\\$In an ideal transformer, the voltage ratio is directly related to the turns ratio. The formula is:$\\ \frac{V_s}{V_p} = \frac{N_s}{N_p} \\$Given:$\\ \frac{N_p}{N_s} = \frac{1}{2} \\$This implies:$\\ N_s = 2N_p \\$Substitute $N_s = 2N_p$ into the voltage ratio formula:$\\ \frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{2N_p}{N_p} \\$Simplify the expression:$\\ \frac{V_s}{V_p} = 2 \\$Therefore, the ratio $\frac{V_s}{V_p}$ is $2:1. \\$This corresponds to Option 4.