Two thin lenses,when in contact,produce a combination of power $+10 \, D$. When they are $0.25 \, m$ apart,the power reduces to $+6 \, D$. The focal lengths of the lenses (in $m$) are

The size of the image of an object at infinity, formed by a convex lens of focal length $30 \,cm$, is $2 \,cm$. If a concave lens of focal length $20 \,cm$ is placed between the convex lens and the image at a distance of $26 \,cm$ from the convex lens, what is the new size of the image (in $\,cm$)?

Two lenses of power $3\,D$ and $-5\,D$ are combined to form a compound lens. An object is placed at a distance of $50\,cm$ from this combination. At what distance (in $cm$) will the image be formed?

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:

$A$ 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:

Two thin lenses of focal lengths $20 \ cm$ and $25 \ cm$ are placed in contact. The effective power of the combination is (in $D$)