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 $$u, v$$ and $$f$$ 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 AB 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 '$$d$$' distance apart. A point object is kept at a distance of $$30 \mathrm{~cm}$$ in front of lens A. Find the value of '$$d$$' so that the rays emerging from lens $B$ are parallel to its principal axis.