Two metallic wires \( P \) and \( Q \) have the same volume and are made of the same material. If their areas of cross-section are in the ratio \( 4 : 1 \) and a force \( F_1 \) is applied to \( P \), producing an extension of \( \Delta l \), the force required to produce the same extension in \( Q \) is \( F_2 \).The value of \( \frac{F_1}{F_2} \) is _______.