Question

(a) Explain the following terms related to spherical lenses :
(i) optical centre
(ii) centres of curvature
(iii) principal axis
(v) principal focus
(vi) focal length
(b) A converging lens has focal length of 12 cm. Calculate at what distance should the object be placed from the lens so that it forms an image at 48 cm on the other side of the lens.

Answer 1

(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.  

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(b) Given: Convex lens (converging lens) Focal length of the lens f = +12 cm Image distance, v= +48 cm Applying the lens formula:

Answer 2

Definitions; Distance of the image = 16 cm

Explanation:

A) Definitions

1. Optical center is the point on lens that lines on the principal axis and rays of light pass through it without deflection.
2. Centre of curvature is the center of the sphere of the lens surface, of which the lens is a part. Since a lens has two spherical surface, lens has two two centers of curvatures.
3. Principal axis is the straight line that passes through the center of curvatures.
4. Aperture is defined as the diameter of the boundary of the circular lens.
5. Principal focus is the point at which a beam of light that is parallel to principal axis will converge/diverges after refraction.  
6. Focal length is the distance between the optical center and principal focus of the lens.

B) Converging (Convex) lens has focal length f = +12 cm

Distance of the image v = +48 cm

1/f = 1/v - 1/u

1/12 = 1/48 - 1/u

1/u = 1/48 - 1/12

  = 3/48

1/u  = 1/16

Hence u = 16 cm

Distance of the object from the convex lens = 16 cm