Two lenses of power $-1.6 D$ and $+2.1 D$ respectively are placed in contact. The focal length of the combination is (in $cm$)

Two planoconvex lenses each of focal length $10 \, cm$ and refractive index $3/2$ are placed as shown. In the space left, water $(R.I = 4/3)$ is filled. The whole arrangement is in air. The optical power of the system is (in diopters):

In a certain camera,a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power $(p)$ and magnification $(m)$ for each lens will be,respectively

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

$A$ plano-convex lens (focal length $f_2,$ refractive index $\mu_2,$ radius of curvature $R$) fits exactly into a plano-concave lens (focal length $f_1,$ refractive index $\mu_1,$ radius of curvature $R$). Their plane surfaces are parallel to each other. Then,the focal length of the combination will be

The focal length (in $cm$) of a lens with dispersive power $0.45$ that should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to form an achromatic combination is: