NDA Physics · Light and Optics

The Human Eye and Optical Instruments

The eye is a variable-focus converging lens that forms a real, inverted image on the retina; accommodation adjusts its focal length. Its defects (myopia, hypermetropia, presbyopia, cataract) each have a standard correction. Microscopes use two convex lenses; telescopes magnify by f_objective / f_eyepiece.

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Why this matters

Thirteen PYQs, mostly recall. The recurring tests are: accommodation as the variable-focus mechanism, the four defects and their corrective lenses (myopia → concave, hypermetropia → convex), the lens-power calculation for a defect, and the microscope/telescope facts — two convex lenses, larger objective focal length in a telescope, and the magnification rules. The one HARD question is a multi-statement microscope-vs-telescope item.

Concept 1 of 3: The human eye and accommodation

The eye works like a camera with a self-adjusting lens. Light enters through the cornea, passes the pupil (whose size the iris controls), and is focused by the crystalline lens onto the retina, forming a real, inverted, diminished image. To keep near and far objects both in focus, the lens changes its own focal length — that automatic refocusing is called accommodation.

Definition

The eye is a converging optical system: cornea + crystalline lens focus light to a real, inverted, diminished image on the retina.

Accommodation: the ciliary muscles change the shape (and hence focal length) of the lens, so objects at different distances and illuminations all focus on the retina. The eye is a lens of variable focal length and variable aperture (the iris/pupil sets the aperture).
The eye uses a converging (convex) lens system — it is NOT a diverging system.
Near point ≈ 25 cm (least distance of distinct vision); far point = infinity for a normal eye.

The eye is a variable-focus converging system. Ciliary muscles change the lens shape (accommodation) so objects at different distances all focus sharply on the retina.

Worked example

Why can a healthy human eye see both a book held close and a distant hill clearly without any external help?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

NDA · Sep 2022 · Q75Moderate

Example 1 · Light and Optics · Human Eye and Optical Instruments

Human eye can see objects at different distances with contrasting illuminations. This is due to

The eye is a CONVERGING system, not a diverging one

The eye focuses light to a real image, so its lens system is convex/converging. Any statement calling the eye a diverging-lens system is the false one.

Drill 1 more on the human eye and accommodation

Concept 2 of 3: Eye defects and their corrections

Four common defects come up again and again, and each has one standard fix. Myopia (short-sight) can't see far — correct with a concave lens. Hypermetropia (long-sight) can't see near — correct with a convex lens. Presbyopia is age-related loss of accommodation — correct with bifocals. Cataract is a clouded lens — fixed by surgery, not a lens. Learn the four pairings cold.

Definition

Each defect has a single standard correction. For myopia (far point at distance d), the corrective lens has power $P = -1/d$ (d in metres) — a concave lens that shifts the far point back to infinity.

Defect	Problem	Correction
Myopia (short / near-sightedness)	Cannot see DISTANT objects clearly; image of a distant object focuses BEFORE the retina; far point is finite	Concave (diverging) lens Myopia = sees near clearly, far blurred. Power P = −1/(far point in m).
Hypermetropia (long / far-sightedness)	Cannot see NEAR objects clearly; image focuses behind the retina	Convex (converging) lens
Presbyopia	Age-related loss of accommodation; both near and far affected	Bifocal lens
Cataract	Eye lens becomes cloudy/opaque	Surgery (lens replacement) — not a spectacle lensQ

Myopia → concave, Hypermetropia → convex, Presbyopia → bifocal, Cataract → surgery. The match-list pairing is tested almost every year.

Practice this conceptself-check · 5 quick reps

The same idea in a real exam question:

NDA · Sep 2023 · Q85Moderate

Example 2 · Light and Optics · Human Eye and Optical Instruments

Ramesh cannot see distinctly objects kept beyond 2 m. This defect can be corrected by using a lens of power

Myopia → concave; hypermetropia → convex (don't swap)

Short-sight (myopia) over-converges, so it needs a DIVERGING (concave) lens. Long-sight (hypermetropia) under-converges, so it needs a CONVERGING (convex) lens. Swapping these two is the classic match-list trap.

Cataract is surgery, not a lens

A clouded lens cannot be fixed by spectacles — it needs surgery. In a disease-remedy match list, pair cataract with surgery, never with a lens.

Drill 4 more on eye defects and their corrections

Concept 3 of 3: Microscope and telescope

Both instruments use two lenses — an objective near the object and an eyepiece near the eye. A microscope magnifies tiny nearby things, so it wants a SHORT objective focal length. A telescope magnifies distant things, so it wants a LONG objective focal length and a short eyepiece. The telescope's magnification is simply the ratio of those two focal lengths.

Definition

Compound microscope: two convex lenses (objective + eyepiece). Magnification rises as the objective focal length DECREASES and as the eyepiece focal length decreases. A short objective focal length is wanted.
Refracting telescope: objective has a larger focal length and larger aperture than the eyepiece. Magnification (normal adjustment) $M = \dfrac{f_o}{f_e}$ — it INCREASES with a larger objective focal length and a smaller eyepiece focal length.
A reflecting telescope (e.g. Newtonian) uses mirrors only, no lenses.

Telescope magnification (normal adjustment)

M = \dfrac{f_o}{f_e}

f_ofocal length of the objective
f_efocal length of the eyepiece

Worked example

A telescope's objective has focal length 100 cm and its eyepiece 5 cm. What is its magnifying power in normal adjustment?

Practice this conceptself-check · 5 quick reps

The same idea in a real exam question:

NDA · Sep 2018 · Q94Hard

Example 3 · Light and Optics · Human Eye and Optical Instruments

Consider the following statements about a microscope and a telescope : 1. Both the eyepiece and the objective of a microscope are convex lenses. 2. The focal length of the objective of a telescope is larger than the focal length of its eyepiece. 3. The magnification of a telescope increases with the increase in focal length of its objective. 4. The magnification of a microscope increases with the increase in focal length of its objective. Which of the statements given above are correct?

Microscope wants a SHORT objective; telescope wants a LONG one

Microscope magnification rises as the objective focal length DECREASES (statement 'increases with objective f' is false). Telescope magnification rises as the objective focal length INCREASES. The two instruments pull opposite ways on the objective focal length.

Newtonian telescope = mirrors only

A reflecting (Newtonian) telescope contains no lenses — only mirrors. Galilean and Keplerian telescopes use lenses. Watch the 'only mirrors' phrasing.

Drill 5 more on microscope and telescope

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Microscope and telescope
Telescope magnification (normal adjustment)
$M = \dfrac{f_o}{f_e}$

Reference tables (1)

Eye defects and their corrections4 rows

Defect	Problem	Correction
Myopia (short / near-sightedness)	Cannot see DISTANT objects clearly; image of a distant object focuses BEFORE the retina; far point is finite	Concave (diverging) lens Myopia = sees near clearly, far blurred. Power P = −1/(far point in m).
Hypermetropia (long / far-sightedness)	Cannot see NEAR objects clearly; image focuses behind the retina	Convex (converging) lens
Presbyopia	Age-related loss of accommodation; both near and far affected	Bifocal lens
Cataract	Eye lens becomes cloudy/opaque	Surgery (lens replacement) — not a spectacle lensQ

Myopia → concave, Hypermetropia → convex, Presbyopia → bifocal, Cataract → surgery. The match-list pairing is tested almost every year.

Watch out for (5)

The eye is a CONVERGING system, not a diverging one
→ The human eye and accommodation
Myopia → concave; hypermetropia → convex (don't swap)
→ Eye defects and their corrections
Cataract is surgery, not a lens
→ Eye defects and their corrections
Microscope wants a SHORT objective; telescope wants a LONG one
→ Microscope and telescope
Newtonian telescope = mirrors only
→ Microscope and telescope

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