Two thin convex lenses are kept in contact coaxially. If the focal length of the combination of the lenses is $4 \ cm$ and the sum of the focal lengths of the two lenses is $18 \ cm$,then the focal length of the lens of lower power is (in $cm$)

Two convex lenses of focal length $20\,cm$ each are placed coaxially with a separation of $60\,cm$ between them. The image of the distant object formed by the combination is at $...........\,cm$ from the first lens.

$A$ beam of parallel rays is brought to a focus by a plano-convex lens. $A$ thin concave lens of the same focal length is joined to the first lens. The effect of this is:

Two lenses of power $6D$ and $-2D$ are combined to form a single lens. The focal length of this lens will be (in $m$)

$A$ thin convex lens of focal length $5 \ cm$ and a thin concave lens of focal length $4 \ cm$ are combined together (without any gap) and this combination has magnification $m_1$,when an object is placed $10 \ cm$ before the convex lens. Keeping the positions of the convex lens and object undisturbed,a gap of $1 \ cm$ is introduced between the lenses by moving the concave lens away,which leads to a change in the magnification of the total lens system to $m_2$. The value of $\left|\frac{m_1}{m_2}\right|$ is . . . . . . .

$A$ bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surfaces are of the same radius of curvature $R = 14 \, cm$. For this bi-convex lens,for an object distance of $40 \, cm$,the image distance will be.......$cm$