Optics Lab · all topics

Module 06 · JEE Main + NEET focus

Optical instruments — lenses with a job

Everything an instrument does is angle inflation: your eye judges size by the angle a thing subtends, so a good instrument delivers the same object at a fatter angle. One lens makes a magnifier, two make a microscope or a telescope — and the eye itself is the one instrument you recalibrate with spectacles.

D = 25 cm (near point) throughout diagrams not to scale — the numbers are

01 — one lens, held close

The simple magnifier

Unaided, the biggest angle you can give an object is to hold it at the near point, D = 25 cm. A convex lens lets you bring it inside its focus instead: the eye sees an erect, virtual, enlarged image. Park that image at the near point for maximum power, or at infinity for a relaxed eye.

image parked at:

angular magnification{{ magMtxt }}

object sits at{{ magUtxt }}

image at{{ magVtxt }}

m = {{ magFormulaPre }} Df

focal length f{{ magFtxt }}

Shorter f = stronger magnifier — but past m ≈ 10 a single lens distorts badly. To go further you magnify twice: that is the compound microscope, next.

02 — magnify, then magnify the magnified

The compound microscope

The objective (tiny f₀) sits just beyond its focus from the object and throws a real, inverted, enlarged image down the tube. The eyepiece then treats that image as its own object — a magnifier on a magnification. Set for a relaxed eye, the intermediate image lands exactly on the eyepiece focus.

total magnification{{ micMtxt }}

object at u₀{{ micUtxt }}

image at v₀{{ micVtxt }}

objective m₀{{ micM0txt }}

eyepiece mₑ{{ micMEtxt }}

M = v₀u₀ · Dfₑ

objective f₀{{ micFotxt }}

eyepiece fₑ{{ micFetxt }}

tube length L{{ micLtxt }}

Exam shortcut: with u₀ ≈ f₀ and v₀ ≈ L, M ≈ (L/f₀)(D/fₑ). Focused at the near point instead, the eyepiece term grows to 1 + D/fₑ.

03 — angle inflation for the sky

The astronomical telescope

A star is not too small — it is too far: its light arrives as a parallel beam at a tiny angle α. The long-focus objective turns angle into a real image of height f₀·α at its focal plane; the short-focus eyepiece turns that height back into an angle β = h/fₑ. The eye wins by m = β/α = f₀/fₑ.

magnifying power{{ telMtxt }}

tube length{{ telLtxt }}

adjustmentnormal (∞ → ∞)

m = f₀fₑ · L = f₀ + fₑ

objective f₀{{ telFotxt }}

eyepiece fₑ{{ telFetxt }}

Focused at the near point instead: m = (f₀/fₑ)(1 + fₑ/D) — slightly bigger, but the eye strains.

Why the big ones are mirrors — the reflecting telescope

◦ A mirror objective has no chromatic aberration — reflection treats every colour alike.

◦ A mirror can be supported from behind, so apertures grow to metres: more light and finer resolution (θ_min = 1.22λ/a).

◦ In the Cassegrain design a small secondary mirror folds the light back through a hole in the primary — a long f₀ in a short tube.

◦ Magnification is still m = f₀/fₑ; aperture buys brightness and detail, not magnification.

04 — the instrument you were issued

The eye & defects of vision

The eye is a ~60 D converging system focusing onto a fixed screen, the retina; the lens accommodates by changing shape. When the geometry is off, the focus misses the retina — and a spectacle lens simply moves the world to where the eye can already see it.

eye:

corrective lens{{ eyePowerTxt }}

far point of this eye{{ eyeFarTxt }}

near point of this eye{{ eyeNearTxt }}

Myopia: eyeball too long — distant light focuses short of the retina; a concave lens (f = −far point) fixes it. Hypermetropia: too short — near objects focus behind; a convex lens brings 25 cm within reach. (Trimmed from the latest NCERT, kept here — teachers still teach it.)

05 — practice arena

Now you work

A warm-up, then an exam bank tagged [JEE Main], [NEET] or [JEE Adv] so you know what each question is calibrated to.

Warm-up 4 quick checks

Q{{ q.n }}. {{ q.q }}

Exam bank 10 single-correct · tagged by exam · {{ examSolved }}/10 correct

Q{{ q.n }}. {{ q.tag }} {{ q.q }}

Recap card — instruments

◦ Magnifier: m = 1 + D/f (near point), D/f (relaxed).

◦ Microscope: M = (v₀/u₀)(D/fₑ) ≈ (L/f₀)(D/fₑ).

◦ Telescope: m = f₀/fₑ, tube = f₀ + fₑ (normal adjustment).

◦ Mirrors beat lenses for big scopes: no chromatic aberration, huge a.

◦ Myopia → concave, f = −(far point); hypermetropia → convex, 1/f = 1/D − 1/(near point).

◦ Aperture buys resolution & brightness; focal ratio buys magnification.

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