CDS (II) 2022 General Knowledge · Question 84 of 120

Correct — D, at infinity. Put a point source exactly at the focus of a converging lens and the rays that pass through emerge parallel to one another, so they never meet at any finite distance — the image is formed at infinity. The lens formula says the same thing in one line. With the object distance equal to the focal length, 1/v equals 1/f plus 1/(minus f), which is zero, so v is infinite. This is simply the reverse of the everyday case in which parallel rays from a distant object are brought to a point at the focus, and it is the arrangement used in a collimator and in the eyepiece of a telescope adjusted for a relaxed eye.

• (a)at the focus on the same side. — A converging lens sends light onward, not back; for a real object it can only form a real image on the far side, or a virtual one on the near side when the object is nearer than the focus. Nothing is formed at the focus on the object's own side.
• (b)at the focus on the opposite side. — The exact reverse of this situation. An object at infinity gives an image at the focus; an object at the focus gives an image at infinity. Swapping the two is the commonest error on this question.
• (c)coincident with the lens. — An image at the lens would mean v equals zero, which the lens formula produces only when the object itself is at the lens. It is not what an object at the focal point does.

For a thin lens the formula 1/v minus 1/u equals 1/f ties the object distance, the image distance and the focal length together, with distances measured from the optical centre and signs taken along the direction of incident light. Feeding in the standard object positions gives the whole table a candidate needs: beyond twice the focal length gives a real, inverted, diminished image between the focus and twice the focus; at twice the focal length gives a real, inverted, same-size image at twice the focus on the other side; between the focus and twice the focus gives a real, inverted, enlarged image beyond twice the focus; at the focus gives an image at infinity; and inside the focus gives a virtual, erect, enlarged image on the same side.

You do not need the algebra if you remember that a lens is reversible. Light from a distant object arrives as a parallel beam and is brought to the focus; run the light the other way and a source at the focus must send out a parallel beam. Parallel rays meet only at infinity, which settles the answer. The bank's entry for this question carries an image flag, but the stem as printed is complete and self-contained and needs no figure to be answered.

• The thin-lens formula is 1/v minus 1/u equals 1/f, with distances measured from the optical centre.
• An object at the focus of a convex lens gives an image at infinity; an object at infinity gives an image at the focus.
• Rays leaving a point at the focus emerge from the lens parallel to one another.
• An object between the focus and twice the focal length gives a real, inverted and enlarged image beyond twice the focal length.
• An object placed at twice the focal length gives a real, inverted, same-size image at twice the focal length on the other side.

• Swapping the two reciprocal cases — object at infinity against object at the focus.
• Applying the mirror formula's sign rules to a lens.
• Assuming a convex lens always makes a real image; inside the focus it does not.

As a where-is-the-image item like this one, or as a short numerical fixing the object distance from the focal length and the nature of the image wanted.

• practice — not a real PYQ

  An object placed at infinity in front of a convex lens forms its image at which one of the following positions?

  • (a)At the optical centre
  • (b)At the focus on the far side
  • (c)At twice the focal length
  • (d)At infinity on the far side

  Answer(b) At the focus on the far side — the reverse of the case in this question, since a lens works equally well in either direction.

• practice — not a real PYQ

  For a convex lens, an object placed between the focus and twice the focal length gives an image that is

  • (a)virtual, erect and diminished
  • (b)real, inverted and of the same size
  • (c)real, inverted and enlarged
  • (d)virtual, erect and of the same size

  Answer(c) real, inverted and enlarged — and it is formed beyond twice the focal length on the far side.