On this page
Questions on the human eye look like biology but are really lens problems. Once you know where the near point and far point are, the power of a correcting lens follows from the lens formula. This post explains how the eye focuses, what goes wrong in each common defect, and how to calculate the correction without sign errors.
How does the eye focus on near and far objects?
The NCERT Class 10 chapter The Human Eye and the Colourful World explains that the ciliary muscles change the curvature, and so the focal length, of the eye lens. This ability is called the power of accommodation. For a young adult with normal vision, the near point is about 25 cm and the far point is at infinity, so the eye sees clearly anywhere between them.
The topic is part of CBSE Class 10 Science. The JEE (Main) 2026 syllabus does not list the eye, but its optics unit does list the thin lens formula and power of a lens, which are exactly the tools used here.
What causes myopia and hypermetropia?
NCERT describes three common refractive defects.
Myopia (near-sightedness). The far point is nearer than infinity, and the image of a distant object forms in front of the retina. It may arise from too much curvature of the eye lens or an elongated eyeball. A concave lens corrects it.
Hypermetropia (far-sightedness). The near point is farther than 25 cm, and light from a near object focuses behind the retina. It arises when the focal length of the eye lens is too long or the eyeball is too small. A convex lens corrects it.
Presbyopia. With age the power of accommodation falls and the near point recedes. Some people need bifocal lenses, with a concave part on top and a convex part below.
These defects are common. The WHO fact sheet on blindness and vision impairment estimates that at least 2.2 billion people have a near or distance vision impairment, and names refractive errors and cataracts as the leading causes. A meta-analysis by Holden and colleagues (2016) estimated that 22.9% of the world population had myopia in 2000 and projected 49.8% by 2050.
Worked example 1: correcting myopia
A student's far point is 2.0 m. What lens lets her see distant objects clearly?
The lens must take an object at infinity and form a virtual image at her far point, 200 cm in front of the eye. With the sign convention, u = −∞ and v = −200 cm.
1/f = 1/v − 1/u = 1/(−200) − 0 = −1/200, so f = −200 cm = −2.0 m.
Power P = 1/f (in metres) = 1/(−2.0) = −0.5 D. The negative sign tells you it is a concave lens.
Worked example 2: correcting hypermetropia
A person's near point is 50 cm. What lens lets him read a book held at 25 cm?
The lens must take an object at 25 cm and form a virtual image at 50 cm, on the same side. So u = −25 cm and v = −50 cm.
1/f = 1/v − 1/u = 1/(−50) − 1/(−25) = −1/50 + 2/50 = +1/50, so f = +50 cm = +0.50 m.
P = 1/0.50 = +2.0 D, a convex lens.
Common mistakes and how to avoid them
Using centimetres in P = 1/f. Power in dioptres needs f in metres. An f of −200 cm is −2.0 m, giving −0.5 D, not −0.005.
Swapping u and v. The object is what the person looks at; the image is where their eye can focus.
Positive v for a virtual image. Both images here are on the object's side, so v is negative.
Mixing up the defects. Myopic people see near objects; their problem is far objects. The prefix "near-sighted" describes what they can see, not what they cannot.
For lens combinations and the lens maker's formula, see our post on lens maker's formula and lens combinations. For sign-convention habits across mirrors and lenses, read ray optics mistakes.
A note on real eye care
This post is about the physics in your syllabus. It is not medical advice. If you have blurred vision, headaches while reading or trouble seeing the board, see an optometrist or eye doctor for a proper eye test. The calculations here are simplified, and real prescriptions involve more than one number.
A practice routine
Write the near point and far point for a normal, myopic and hypermetropic eye from memory.
Solve four correction problems: two myopia and two hypermetropia, each time writing u and v with signs before using the formula.
Solve the NCERT exercise on a bifocal prescription and explain which part of the lens does what.
Draw the ray diagram for each defect, with and without the correcting lens.
If you are unsure whether your gap is the lens formula or the sign convention, Fermi's AI tutor can work out what you already know and build a plan for the session, so you start at the step that is actually missing.
Tonight, change the far point in example 1 to 80 cm and check that you get −1.25 D.
