1. The problem is to convert the time durations 30 minutes and 2 hours into a ratio. 2. First, convert all times to the same unit for an accurate ratio comparison. Since 1 hour = 60 minutes, 2 hours = 2 \times 60 = 120 minutes. 3. Now express the ratio as $30$ minutes to $120$ minutes. 4. The ratio is therefore $30:120$. 5. Simplify the ratio by dividing both terms by their greatest common divisor, which is 30. 6. Dividing both sides by 30 gives $\frac{30}{30}:\frac{120}{30} = 1:4$. 7. The final simplified ratio of 30 minutes to 2 hours is $\boxed{1:4}$.