Two similar plano-convex lenses are combined | vedclass

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(B) When two thin lenses with focal lengths $f_1$ and $f_2$ are placed in contact,the equivalent focal length $F$ is given by $\frac{1}{F} = \frac{1}{

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$1:1:1$

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(B) When two thin lenses with focal lengths $f_1$ and $f_2$ are placed in contact,the equivalent focal length $F$ is given by $\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$.In each of the three cases shown,we are combining two identical plano-convex lenses,each having a focal length $f$. For case $1$: The lenses are combined to form a biconvex lens. The power is $P = P_1 + P_2 = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}$,so $F_1 = \frac{f}{2}$.For case $2$: The lenses are combined such that their curved surfaces face the same direction. The power is $P = P_1 + P_2 = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}$,so $F_2 = \frac{f}{2}$.For case $3$: The lenses are combined such that their curved surfaces face each other. The power is $P = P_1 + P_2 = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}$,so $F_3 = \frac{f}{2}$.Since $F_1 = F_2 = F_3$,the ratio of the focal lengths is $1:1:1$.

Two similar plano-convex lenses are combined together in three different ways as shown in the figure. The ratio of the focal lengths in the three cases will be

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