Two identical symmetric double convex lenses of focal length \( f \) are cut into two equal parts \( L_1, L_2 \) by the AB plane and \( L_3, L_4 \) by the XY plane as shown in the figure respectively. The ratio of focal lengths of lenses \( L_1 \) and \( L_3 \) is:
Show Hint
When symmetric lenses are cut into two equal parts, the focal length of the new lenses is halved compared to the original lens.
When a lens is divided into two equal sections, its focal length is altered. The focal length of each resulting part is given by the formula:
\[f_{\text{new}} = \frac{f}{2}\]
Lenses \( L_1 \) and \( L_2 \) retain their original focal length \( f \). However, for lenses \( L_3 \) and \( L_4 \), which are bisected by the XY plane, their focal length is halved. Consequently, the ratio of the focal lengths of \( L_1 \) to \( L_3 \) is:
\[\frac{f_1}{f_3} = \frac{f}{2f} = \frac{1}{2}\]
The resultant ratio is \( \boxed{1 : 2} \).
