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(D) When two thin lenses are placed in contact,the effective focal length $F$ is given by the formula $\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$.In

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$1: 1: 1$

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(D) When two thin lenses are placed in contact,the effective focal length $F$ is given by the formula $\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$.In all three cases shown,we have two plano-convex lenses,each with focal length $f$. When they are placed in contact,the combination acts as a single lens system.Case $(i)$: The two lenses are in contact with their curved surfaces facing the same direction. The effective focal length is $\frac{1}{F_1} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}$,so $F_1 = \frac{f}{2}$.Case $(ii)$: The two lenses are in contact forming a biconvex lens. The effective focal length is $\frac{1}{F_2} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}$,so $F_2 = \frac{f}{2}$.Case $(iii)$: The two lenses are in contact with their curved surfaces facing each other. The effective focal length is $\frac{1}{F_3} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}$,so $F_3 = \frac{f}{2}$.Thus,the ratio of their effective focal lengths is $F_1 : F_2 : F_3 = \frac{f}{2} : \frac{f}{2} : \frac{f}{2} = 1 : 1 : 1$.

Two thin plano-convex lenses each of focal length $f$ are placed as shown in the figure. The ratio of their effective focal lengths in the three cases is

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