JEE Mains Physics · Ray Optics

Optical Instruments and the Eye

A compound microscope magnifies by (L/fₒ)(D/fₑ) in normal adjustment, a telescope by fₒ/fₑ with its lenses fₒ + fₑ apart, and resolving power grows with the aperture and falls with the wavelength.

All Ray Optics notes JEE Mains Physics strategy

Why this matters

Twelve PYQs, ten of them multiple choice, and four from 2026. Seven are about magnifiers, microscopes and telescopes: the magnification in normal adjustment, the length of a telescope, a beam expander and the job of a reflecting telescope's second mirror. Five are about seeing detail: resolving power, a camera's focal length, and the defects of the eye and the lenses that correct them.

Concept 1 of 2: Magnification of microscopes and telescopes

Both instruments use two converging lenses, for opposite jobs. A microscope's objective has a short focal length and makes a large real image of a near object; the eyepiece then works as a magnifying glass on that image. A telescope's objective has a long focal length and makes a small real image of a distant object at its focus; the eyepiece magnifies the angle. In normal adjustment the final image is at infinity, so the eye is relaxed.

Definition

Simple microscope: the gain comes from bringing the object closer than D = 25 cm; at the eye, the image subtends the same angle as the object. $M = D/f$ with the image at infinity, $1 + D/f$ with the image at D.
Compound microscope, normal adjustment: $M = \dfrac{L}{f_o} \times \dfrac{D}{f_e}$ , with L the tube length.
Refracting telescope, normal adjustment: $M = \dfrac{f_o}{f_e}$ , length $f_o + f_e$ . A wider objective gathers more light and resolves finer detail; it does not change M.
Beam expander: two converging lenses with a common focus, $f_1 + f_2$ apart; output width over input width is $f_2/f_1$ .
Reflecting telescope: a concave mirror is the objective; a small secondary mirror sends the light out of the tube to the eyepiece.

Instrument	First element	Magnification, final image at infinity	Distance between the elements
Simple microscope	One short-focus convex lens	$D/f$	Only one lens
Compound microscope	Short-focus objective lens	$\dfrac{L}{f_o}\cdot\dfrac{D}{f_e}$	Set by the tube length L
Refracting telescope	Long-focus objective lens	$f_o/f_e$	$f_o + f_e$
Reflecting telescope	Concave mirror, $f_o = R/2$	$f_o/f_e$	A secondary mirror folds the light to an eyepiece outside the tube
Beam expander	Convex lens of focal length $f_1$	Beam width multiplied by $f_2/f_1$	$f_1 + f_2$

D = 25 cm, the least distance of distinct vision. Normal adjustment puts the final image at infinity.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2026 · 21 Jan 2026 Shift 1 · Q25Moderate

Example 1 · Ray Optics · Optical Instruments and the Eye

In a microscope the objective is having focal length

f_{0} = 2\text{ }cm

and eye-piece is having focal length

f_{e} = 4\text{ }cm

. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is

\_\_\_\_

A telescope's M is fₒ/fₑ, not fₑ/fₒ

The objective has the long focal length. Inverting the ratio gives a magnification below 1, which is never an option for a working telescope.

A wider objective does not raise the magnification

A larger aperture lets in more light and resolves more detail, but in normal adjustment M depends only on the focal lengths.

Normal adjustment uses D/fₑ, not 1 + D/fₑ

The extra 1 appears only when the final image is at the near point. Read where the final image is before choosing the formula.

Drill 6 more on magnification of microscopes and telescopes

Concept 2 of 2: Resolving power and defects of vision

A lens of finite size cannot make a point image: diffraction blurs it. Two points can be told apart only if their blurs do not overlap too much. A wider aperture and a shorter wavelength make the blur smaller. The eye has its own limits: the range from its near point to its far point, which spectacles correct.

Definition

Telescope: smallest resolvable angle $\theta = \dfrac{1.22\lambda}{D}$ ; resolving power $\dfrac{D}{1.22\lambda}$ , with D the aperture.
Microscope: resolving power $\dfrac{2\mu\sin\theta}{1.22\lambda}$ . A liquid of larger μ between the object and the objective improves it.
Camera photographing a distant scene: image size over object size equals f over the distance, so $f = \text{distance} \times \dfrac{\text{film size}}{\text{scene size}}$ .
Myopia: the far point is too close; a concave lens of focal length equal to minus the far-point distance corrects it.
Hypermetropia: the near point is too far; a convex lens forms, at the person's near point, a virtual image of an object at 25 cm.
Astigmatism: the cornea curves differently in different planes, so lines in one direction blur or look distorted; a cylindrical lens corrects it.

Defect	What goes wrong	Correcting lens	How to find the lens
Myopia (short sight)	Far point closer than infinity	Concave	$f = -(\text{far-point distance})$
Hypermetropia (long sight)	Near point farther than 25 cm	Convex	It images an object at 25 cm onto the near point
Presbyopia	The near point recedes with age as focusing weakens	Convex for reading, often in a bifocal	As for hypermetropia
Astigmatism	Unequal curvature of the cornea; lines in one direction blur	Cylindrical	Shaped to correct the faulty plane only

A reading glass is tested at the near point: an object at 25 cm must appear at the person's own near point.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2023 · 30 January 2023 · Q4Moderate

Example 2 · Ray Optics · Optical Instruments and the Eye

A person has been using spectacles of power -1.0 dioptre for distant vision and a separate reading glass of power 2.0 dioptres. What is the least distance of distinct vision for this person:

Resolving power is not magnification

A stronger eyepiece enlarges the blur too. Only a wider aperture, a shorter wavelength or, in a microscope, a denser medium in front of the objective resolves finer detail.

A reading glass forms a virtual image

It images an object at 25 cm onto the person's near point, on the same side as the object. So v is negative and farther from the lens than 25 cm.

Blurred is not the same as distorted

Distant objects that look blurred point to myopia. Lines that look uneven or distorted point to astigmatism, which needs a cylindrical lens.

Drill 4 more on resolving power and defects of vision

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.

Reference tables (2)

Magnification of microscopes and telescopes5 rows

Instrument	First element	Magnification, final image at infinity	Distance between the elements
Simple microscope	One short-focus convex lens	$D/f$	Only one lens
Compound microscope	Short-focus objective lens	$\dfrac{L}{f_o}\cdot\dfrac{D}{f_e}$	Set by the tube length L
Refracting telescope	Long-focus objective lens	$f_o/f_e$	$f_o + f_e$
Reflecting telescope	Concave mirror, $f_o = R/2$	$f_o/f_e$	A secondary mirror folds the light to an eyepiece outside the tube
Beam expander	Convex lens of focal length $f_1$	Beam width multiplied by $f_2/f_1$	$f_1 + f_2$

D = 25 cm, the least distance of distinct vision. Normal adjustment puts the final image at infinity.

Resolving power and defects of vision4 rows

Defect	What goes wrong	Correcting lens	How to find the lens
Myopia (short sight)	Far point closer than infinity	Concave	$f = -(\text{far-point distance})$
Hypermetropia (long sight)	Near point farther than 25 cm	Convex	It images an object at 25 cm onto the near point
Presbyopia	The near point recedes with age as focusing weakens	Convex for reading, often in a bifocal	As for hypermetropia
Astigmatism	Unequal curvature of the cornea; lines in one direction blur	Cylindrical	Shaped to correct the faulty plane only

A reading glass is tested at the near point: an object at 25 cm must appear at the person's own near point.

Watch out for (6)

A telescope's M is fₒ/fₑ, not fₑ/fₒ
→ Magnification of microscopes and telescopes
A wider objective does not raise the magnification
→ Magnification of microscopes and telescopes
Normal adjustment uses D/fₑ, not 1 + D/fₑ
→ Magnification of microscopes and telescopes
Resolving power is not magnification
→ Resolving power and defects of vision
A reading glass forms a virtual image
→ Resolving power and defects of vision
Blurred is not the same as distorted
→ Resolving power and defects of vision

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