Two identical thin biconvex lenses of focal length $15 \, cm$ and refractive index $1.5$ are in contact with each other. The space between the lenses is filled with a liquid of refractive index $1.25$. The focal length of the combination is $cm$.

Two lenses having focal lengths in the ratio $f_1:f_2 = 2:3$ are combined to produce no net dispersion. Find the ratio of the dispersive powers of the glasses used.

As shown in the figure,a concave lens of focal length $50 \, cm$ and a convex lens of focal length $25 \, cm$ are placed in contact with each other. If a parallel beam of light is incident on the system,how will it emerge?

Two thin biconvex lenses have focal lengths $f_{1}$ and $f_{2}$. $A$ third thin biconcave lens has a focal length of $f_{3}$. If the two biconvex lenses are in contact,the total power of the lenses is $P_{1}$. If the first convex lens is in contact with the third lens,the total power is $P_{2}$. If the second lens is in contact with the third lens,the total power is $P_{3}$,then:

Two lenses of power $+12 \ D$ and $-2 \ D$ are placed in contact. What will be the focal length of the combination in $cm$?

$A$ real image of an object is formed at a distance of $20 \, cm$ from a lens. On putting another identical lens in contact with it,the image is shifted $10 \, cm$ towards the combination. The power of the lens is (in $, D$)