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

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):

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:

The diagram below shows an object placed at a distance $2f$ in front of a convex lens of focal length $f$. Which of the following represents the positions of the image when $(i)$ a parallel-sided glass block,or $(ii)$ a converging lens of long focal length is inserted between the object and the convex lens?

Two lenses of power $+5 \, D$ are placed at a distance $d$ to form sun goggles. The distance $d$ is . . . . . $cm$.

$A$ bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both curved surfaces have the same radius of curvature $R = 14\, cm$. For this bi-convex lens,for an object distance of $40\, cm$,the image distance will be.....$ cm$