A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between $\mathit{u},\mathit{v}$ and $\mathit{f}$ for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.
(i) An object $\mathit{A}\mathit{B}$ is kept in front of a composite convex lens, as shown in figure. Will the lens produce one image? If not, explain.
(ii) A real image of an object formed by a convex lens is observed on a screen. If the screen is removed, will the image still be formed? Explain.
(iii) A double convex lens is made of glass of refractive index 1.55 with both faces of the same radius of curvature. Find the radius of curvature required if focal length is $20\mathrm{cm}$.
OR
(iii) Two convex lenses A and B of focal lengths $15\mathrm{cm}$ and $10\mathrm{cm}$ respectively are placed coaxially ' $\mathit{d}$ ' distance apart. A point object is kept at a distance of $30\mathrm{cm}$ in front of lens A. Find the value of ' $\mathit{d}$ ' so that the rays emerging from lens $\mathit{B}$ are parallel to its principal axis.