An object is placed at a distance of 30cm from a concave lens of focal length 30cm. (i) Use lens formula to determine the distance of the image from the lens. (ii) List four characteristics of the image (nature, position, size, erect/inverted) in this case. (iii) Draw a labelled diagram to justify your answer in part (ii).

(i) Using the lens formula:

1/f = 1/v - 1/u

where:

f = focal length = -30 cm (concave lens)
u = object distance = -30 cm (object is placed in front of the lens)
v = image distance (to be determined)

Substituting the values:

1/(-30) = 1/v - 1/(-30)

1/v = 1/(-30) + 1/30

1/v = 0

v = ∞

The image is formed at infinity.

(ii) Characteristics of the image:

• Nature: Virtual
• Position: At infinity
• Size: Highly diminished (almost a point)
• Orientation: Erect

(iii) Labelled diagram:

[A diagram should be included here. It would show a concave lens with an object placed at 30cm to the left. Rays from the top of the object would pass through the lens and diverge. The image would be shown as a virtual, highly diminished, erect image at infinity. The principal focus and optical center should be clearly labelled.]

Note: Since the object is placed at the focal point of a concave lens, the image formed is virtual, erect, highly diminished, and at infinity. The lens formula calculation reflects this.