The focal length of a lens of dispersive power $0.45$ which should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to make the achromatic combination from the two lenses,in $cm$ is

The focal length of a combination of lenses formed with lenses having powers of $+2.50 \ D$ and $-3.75 \ D$ will be .... $cm$.

The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal lengths $10 \,cm$ and $15 \,cm$ respectively. The distance between $L_1$ and $L_2$ is: (in $\,cm$)

$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave lens of focal length $20 \ cm$. An object is placed at $20 \ cm$ to the left of this lens system. The distance of the image from the lens in $cm$ is . . . . . .

An achromatic convergent lens of focal length $20 \, cm$ is made of two lenses (in contact) of materials having dispersive powers in the ratio of $1 : 2$ and having focal lengths $f_1$ and $f_2$. Which of the following is true?

An object is placed $0.40 \,m$ from one of the two lenses $L_1$ and $L_2$ of focal lengths $0.20 \,m$ and $0.10 \,m$ respectively,as depicted in the figure. The separation between the lenses is $0.30 \,m$. The final image formed by this two-lens system is at