One plano-convex and one plano-concave lens of same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is $\mu_1$ and that of $2$ is $\mu_2$,then the focal length of the combination is

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

$(a)$ Determine the 'effective focal length' of the combination of two lenses,a convex lens of focal length $30 \; cm$ and a concave lens of focal length $20 \; cm$,if they are placed $8.0 \; cm$ apart with their principal axes coincident. Does the answer depend on which side of the combination a beam of parallel light is incident? Is the notion of effective focal length of this system useful at all?
$(b)$ An object $1.5 \; cm$ in size is placed on the side of the convex lens in the arrangement $(a)$ above. The distance between the object and the convex lens is $40 \; cm$. Determine the magnification produced by the two-lens system,and the size of the image.

$A$ concave lens and a convex lens have the same focal length of $20 \ cm$ and are placed in contact. This combination is used to view an object $5 \ cm$ long kept at $20 \ cm$ from the lens combination. As compared to the object,the image will be:

An effective power of a combination of $5$ identical convex lenses which are kept in contact along the principal axis is $25 \ D$. Focal length of each of the convex lens is: (in $cm$)

Assertion: Two convex lenses joined together cannot produce an achromatic combination.
Reason: The condition for achromatism is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,where symbols have their usual meaning.