CDS (II) 2021 General Knowledge · Question 1 of 120

Correct — C, Between the principal focus and twice the focal length. A convex lens produces an image that is both real and enlarged from exactly one object position, and the standard table of image formation says which. Walk down its rows. An object at infinity gives a point-sized image at the focus. Beyond 2F the image is real but diminished, and lands between F and 2F on the far side. At 2F the image sits at 2F and is exactly the same size as the object. Bring the object inside 2F but keep it outside F, and the image runs out beyond 2F on the other side, real, inverted and larger than the object. Push the object right up to F and no image forms at all, because the rays leave the lens parallel. Inside F the image flips to virtual and erect. Only the fourth row meets both conditions the stem sets. The lens formula gives the same verdict without the table: magnification for a real image is v/u in magnitude, so the image beats the object in size only once the image distance exceeds the object distance, and that happens precisely in the band between F and 2F. It is the setting a slide projector uses — the slide sits a little outside the focus, and the screen far away carries a big real picture.

• (a)At twice the focal length — The 2F position is the boundary case, not an enlarging one. The image forms at 2F on the far side, real and inverted, but the same size as the object.
• (b)At infinity — Rays from an object at infinity arrive parallel and meet at the focus. That image is real, but highly diminished — effectively a point — which is the opposite of what the stem asks for.
• (d)Beyond twice the focal length — Real and inverted, yes, but diminished. The image falls between F and 2F on the other side and is smaller than the object. This is the camera arrangement rather than the projector one.

For a thin convex lens the character of the image depends on one thing only — where the object stands relative to the focus F and the point 2F. Real images form on the far side and are always inverted; virtual images form on the same side and are always erect. Reality and enlargement can be had together at a single object position, the band between F and 2F, and everything else on the table is a consequence of the lens formula 1/v − 1/u = 1/f with magnification m = v/u.

The two conditions in the stem do the sorting between them. Asking for a real image alone would rule out only the inside-the-focus row; asking for an enlarged image alone would rule out the at-2F and beyond-2F rows. Candidates who remember that the table exists but not its ordering usually pick (a), reading 'twice the focal length' as far enough away to magnify. It is the exact dividing line between magnifying and shrinking, which is why examiners like putting it first in the option list. A useful habit is to memorise the two extremes rather than the middle: inside F is the magnifying glass, beyond 2F is the camera, and everything real and enlarged has to live between them.

• An object between F and 2F gives an image beyond 2F on the other side of the lens, real, inverted and enlarged — the only row of the standard table that is both real and enlarged.
• An object at 2F gives an image at 2F, real, inverted and of the same size; this is the boundary between magnification and diminution.
• An object placed inside the focus gives a virtual, erect, enlarged image on the same side of the lens — the magnifying-glass setting.
• A slide projector puts the slide just outside the focal point, which is why the picture on a distant screen is real, enlarged and inverted, and why slides are loaded upside down.
• For a real image, magnification in magnitude is v/u, so the image exceeds the object in size only when the image distance exceeds the object distance.

• Reading 'at twice the focal length' as simply 'far from the lens'. It is the precise same-size position.
• Confusing the magnifying-glass setting (object inside F, image virtual) with the projector setting (object between F and 2F, image real).
• Assuming that any enlarged image must be virtual, or that any real image must be diminished.

Either as a position-to-image-nature match like this one, or as a numerical asking where to place an object of given focal length to get a same-size, diminished or enlarged real image.

• practice — not a real PYQ

  An object is placed 20 cm in front of a convex lens of focal length 10 cm. The image formed is

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

  Answer(b) real, inverted and of the same size — the object is at 2F, so the image forms at 2F on the other side with magnification 1.

• practice — not a real PYQ

  To use a convex lens as a simple magnifying glass, the object must be placed

  • (a)beyond twice the focal length
  • (b)at twice the focal length
  • (c)between the focus and twice the focal length
  • (d)between the optical centre and the focus

  Answer(d) between the optical centre and the focus — only there is the image virtual, erect and enlarged.