Draw a diagram of ‘image formed by concave lens’. 2(b) State the nature of image formed by concave lens. 1(c) If the focal length of a concave lens is 25 cm, find the power of the lens. 2

Answer: (b) The image is virtual, erect and diminished, formed between the optical centre and the focus on the same side as the object; (c) power = –4 D.

(a) Diagram: image formed by a concave lens (object beyond F₁)

                                          concave lens              ////
                                            \|/                /////
                                             |            /////
                                             |       /////
   A                                         |  /////
   ^-----------------------------------------|//
   |   \\\\\\\                        :::::  |
   |          \\\\\\\            :::::       |
   |                 \\\\\\A'::::            |
   |                   :::::^\\\\\\          |
   |              :::::     !      \\\\\\\   |
---------------------------------------------|--------------------------
   B           F1           B'               |O  \\\\\\\
                                             |          \\\\\\\
                                             |                 \\\\\\\
                                            /|\                       \\

  Ray 1 (from A, parallel to axis) diverges after refraction as if coming from F1 (dotted : line).
  Ray 2 (from A, through optical centre O) goes undeviated (\\\ line).
  AB = object;  A'B' = virtual, erect, diminished image between F1 and O.

Construction: (1) a ray from A parallel to the principal axis, after refraction, diverges as if coming from the focus F₁ (shown dotted backwards); (2) a ray from A towards the optical centre O passes undeviated. The refracted rays do not meet; when produced backwards they appear to meet at A′. Drawing A′B′ perpendicular to the axis gives the image A′B′ between F₁ and O on the same side as the object.

(b) Nature of image: virtual, erect and diminished; it is formed between the optical centre O and the focus F₁, on the same side of the lens as the object (for any position of the object).

(c) For a concave lens the focal length is negative: \(f = -25\ \text{cm} = -0.25\ \text{m}\).

\[P = \frac{1}{f\,(\text{in m})} = \frac{1}{-0.25} = -4\ \text{D}\]

The power of the lens is –4 dioptre (negative, as a concave lens is diverging).