For a human eye, where u is the distance of an object from the eye, f is the focal length of the lens and v is the distance of image from the eye, which is the correct schematic graph ?

Correct — C, the plot of f against u that rises and then levels off. The four printed graphs differ in their axis labels, and that is what decides the item: (a) and (b) plot image distance v against object distance u, (c) plots focal length f against u, and (d) plots v against f. The human eye is not a camera that racks its lens back and forth. The retina sits at a fixed distance behind the lens, so the image distance v is essentially constant — about 2·5 cm — no matter how far away the object is. Any graph showing v changing with u is therefore wrong on the physics, which rules out (a), (b) and (d) at once. What the eye changes instead is the focal length, by the ciliary muscles altering the curvature of the lens. This is accommodation. With v held fixed, the lens equation ties f to u: for a near object the lens must be strongly curved and f is short; as the object recedes, f lengthens and approaches the fixed image distance as u tends to infinity. So f rises with u and then flattens towards a limiting value — exactly the shape drawn in (c).

Why the others are wrong

• (a)
  A plot of v against u, falling steeply and then levelling off — This is the correct shape for an ordinary fixed-focus lens, where moving the object changes where the image forms. In the eye the image must always land on the retina, so v does not change.
• (b)
  A plot of v against u, a straight line of negative slope — Wrong on both counts. The lens equation is never linear in u and v, and in the eye v is fixed anyway, so it cannot fall steadily as u increases.
• (d)
  A plot of v against f, rising steeply and then levelling off — The shape is plausible but the axes are not. It again treats v as a variable, whereas in the eye v is the one quantity held constant by the position of the retina.

Accommodation is the eye's power to focus objects at different distances by changing the focal length of its lens rather than its position. The ciliary muscles contract to thicken the lens for near objects, shortening f, and relax to flatten it for distant ones, lengthening f. The image distance stays fixed because the retina does.

Key facts

• In the human eye the image distance v is fixed by the retina, about 2·5 cm.
• Focusing is done by changing the focal length f — accommodation.
• Ciliary muscles thicken the lens for near objects, giving a shorter f.
• As u increases, f increases and approaches the fixed v.
• An ordinary camera does the opposite: f is fixed and the image distance is adjusted.

Common traps

• Reading the curve shapes without checking the axis labels.
• Treating the eye like a camera, with a fixed lens and a moving image plane.
• Assuming the image distance changes when the object moves.

No directly related past PYQ was found.

• practice — not a real PYQ

  The human eye focuses objects at different distances by

  • (a)moving the lens towards or away from the retina
  • (b)changing the focal length of its lens
  • (c)changing the diameter of the eyeball
  • (d)moving the retina
  Answer(b) changing the focal length of its lens — the ciliary muscles alter the lens curvature.
• practice — not a real PYQ

  When a normal eye views a very distant object, the ciliary muscles are

  • (a)fully contracted and f is minimum
  • (b)relaxed and f is maximum
  • (c)contracted and f is maximum
  • (d)relaxed and f is minimum
  Answer(b) relaxed and f is maximum — the lens is at its flattest for distant vision.