$A$ lens of power $3.5 \, D$ is placed in contact with a lens of power $-2.5 \, D$. The combination behaves as:

Obtain the equation of power and magnification for a combination of lenses.

The focal length of the field lens (which is an achromatic combination of two lenses) of a telescope is $90 \ cm$. The dispersive powers of the two lenses in the combination are $0.024$ and $0.036$. The focal lengths of the two lenses are:

$A$ collimated beam of light of diameter $2 \ mm$ is propagating along the $x$-axis. The beam is required to be expanded into a collimated beam of diameter $14 \ mm$ using a system of two convex lenses. If the first lens has a focal length of $40 \ mm$, then the focal length of the second lens is . . . . . . $mm$.

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. The lenses are made of different materials with refractive indices $n_1$ and $n_2$,and $R$ is the radius of curvature of the curved surfaces. What is the focal length of the combination?

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials with refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses,then the focal length of the combination is: