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(a) (i) Optical center is defined as the point on the lens which is on the principal axis and the light ray doesn’t deflect when passes through it.

(ii) Centre of curvature is defined as the center of the surface of sphere of which the lens is a part. Since, a lens has two surfaces, so the lens has two centers of curvatures.

(iii) Principal axis is defined as the straight lines passing through center of curvature.

(iv)Aperture is defined as the diameter of the boundary of the circular lens.

(v) Principal focus is defined as the point where beam of light parallel to principal axis, either converges or diverges after refraction.

(vi) Focal length is defined as the distance between the optical center and principal focus of the lens.

(c) Given: Convex lens (converging lens)

Focal length of the lens f = +12 cm

Image distance, v= +48 cm

Applying the lens formula:

Thus, u=-16 cm

The object should be placed at a distance of 16 cm from the lens.