$A$ combination of two thin lenses of the same material with focal lengths $f_1$ and $f_2$,arranged on a common axis,minimizes chromatic aberration if the distance between them is:

$A$ 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:

As shown in the figure, a combination of a thin plano-concave lens and a thin plano-convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is $30\,cm$ and the refractive index of the material for both the lenses is $1.75$. Both the lenses are placed at a distance of $40\,cm$ from each other. Due to the combination, the image of the object is formed at a distance $x = ..........cm$ from the concave lens.

Find the resultant focal length for the following system where the common radius of curvature is $15 \ cm$. The glass has a refractive index of $1.5$ and water has a refractive index of $\frac{4}{3}$.

$A$ convex lens of focal length $20 \, cm$ is cut into two equal parts. This results in two plano-convex lenses as shown in the figure. These two parts are then placed in contact with each other as shown in the figure. What will be the focal length of the system in $cm$?

An optical device is constructed by fixing three identical convex lenses of focal lengths $10 \,cm$ each inside a hollow tube at equal spacing of $30 \,cm$ each. One end of the device is placed $10 \,cm$ away from a point source. What is the image shift in $cm$ when the device is moved away from the source by another $10 \,cm$?