Two lenses have focal lengths $f_1$ and $f_2$ and their dispersive powers are $\omega_1$ and $\omega_2$ respectively. They will together form an achromatic combination if

$A$ 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:

Two lenses of focal lengths $f_1$ and $f_2$ are placed in contact,and the image is formed at a distance of $60 \, cm$. When the lenses are separated by a distance of $10 \, cm$,the image is formed at a distance of $30 \, cm$. What are the values of $f_1$ and $f_2$?

$A$ convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is $2/3$. Their equivalent focal length is $30 \, cm$. Their individual focal lengths in $cm$ will be

Two plano-convex lenses,each of focal length $10 \, cm$ and refractive index $3/2$,are placed as shown in the figure. The space between them is filled with water $\left( \mu = 4/3 \right)$. The whole arrangement is in air. The optical power of the system is ....... $D$.

The size of the image of an object, which is at infinity, as 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, calculate the new size of the image. (in $cm$)