Optics Formula Sheet — JEE Main Physics

Every key Optics formula, definition and theorem for JEE Main Physics in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 29 sub-topics

Reflection of light
Spherical mirrors
Mirror formula
Refraction of light
Total internal reflection and its applications
Optical fibres
Refraction at spherical surfaces
Lenses
Thin lens formula
Lensmaker's formula
Magnification
Power of a lens
Combination of thin lenses in contact
Refraction and dispersion of light through a prism
Scattering of light - blue colour of sky and reddish appearance of the sun at sunrise and sunset
Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers
Wave optics: wave front and Huygens principle
Reflection and refraction of plane wave at a plane surface using wave fronts
Proof of laws of reflection and refraction using Huygens principle
Interference
Young's double slit experiment and expression for fringe width
Coherent sources and sustained interference of light
Diffraction due to a single slit
Width of central maximum
Resolving power of microscope and astronomical telescope
Polarisation
Plane polarised light
Brewster's law
Uses of plane polarised light and Polaroids

Reflection & Spherical Mirrors

Mirror formula

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}; f = \frac{R}{2}

u =

object dist.,

v =

image dist.,

f =

focal length,

R =

radius; Cartesian sign convention from the pole

Magnification

m = - \frac{v}{u} = \frac{h ^{'}}{h}

m > 0

erect/virtual;

m < 0

inverted/real;

∣ m ∣ > 1

magnified. Object moving along the axis: image velocity

v_{I} = - m^{2} v_{O}

(opposite sense along the axis)

Concave mirror ray diagram: object beyond C forms a real inverted diminished image between F and C — Object beyond C $\to$ real, inverted, diminished.

Comparative: mirror image nature

Mirror / object	Image
Plane	virtual, erect, same size
Convex (any)	virtual, erect, diminished
Concave, beyond F	real, inverted
Concave, within F	virtual, erect, magnified

🚫 Examiner Trap · Mirrors & sign convention

(1) Measure all distances from the

pole

, positive along incident light; real distances come out

negative

. (2)

f < 0

for concave,

f > 0

for convex. (3)

m = - v / u

— the minus sign matters for image orientation. (4) Convex & plane mirrors

never

give a real image.

Refraction & Total Internal Reflection

Snell's law

n_{1} sin θ_{1} = n_{2} sin θ_{2}; n = \frac{c}{v} = \frac{λ _{v a c}}{λ _{m e d}}

rarer

\to

denser bends

toward

the normal; frequency is unchanged on refraction

Apparent depth

\frac{real depth}{apparent depth} = n; shift = t (1 - \frac{1}{n})

t =

slab thickness; object looks raised when viewed from the rarer side

Refraction at a spherical surface

\frac{n _{2}}{v} - \frac{n _{1}}{u} = \frac{n _{2} - n _{1}}{R}

single surface;

R > 0

if centre is on the outgoing side

Left: refraction bending toward the normal entering a denser medium. Right: total internal reflection beyond the critical angle — Refraction vs total internal reflection.

Critical angle (TIR)

sin θ_{c} = \frac{1}{n} = \frac{n _{r a rer}}{n _{d e n ser}}

only

denser \to rarer

, for

i > θ_{c}

🚫 Examiner Trap · Refraction & TIR

(1) On refraction

frequency stays

the same; speed and

λ

change. (2) TIR needs light going

denser \to rarer

AND

i > θ_{c}

— not the reverse. (3) Higher n

\Rightarrow

smaller

θ_{c}

(diamond sparkles,

θ_{c} \approx 2 4^{\circ}

). (4) Apparent depth

<

real depth; the shift is

t (1 - 1/ n)

Lenses & Lensmaker's Formula

Lens formula

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}; m = \frac{v}{u}

note the

minus

sign (vs mirror's plus);

m > 0

erect

Lensmaker's formula

\frac{1}{f} = (n - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})

n =

lens/medium index ratio;

f > 0

convex (converging),

f < 0

concave (diverging)

Convex lens ray diagram: object beyond 2F forms a real inverted image between F' and 2F' — Convex lens: real inverted image (object beyond 2F).

Power & combination

P = \frac{1}{f ( m )} (dioptre); \frac{1}{F} = \frac{1}{f _{1}} + \frac{1}{f _{2}} - \frac{d}{f _{1} f _{2}}

in contact (

d = 0

P = \sum P_{i}

Lens special cases

▸Plano-convex: $f = \frac{R}{n - 1}$ (e.g. $f = 2 R$ for $n = 1.5$ ); equiconvex: $f = \frac{R}{2 ( n - 1 )}$ .
▸Silvered lens (one face mirrored) acts as a mirror: $P_{e q} = 2 P_{l e n s} + P_{mi rror}$ ( $P_{mi rror} = - \frac{1}{f _{m}}$ ). Plano-convex silvered on the plane face: $f = \frac{R}{2 ( n - 1 )}$ ; on the curved face: $f = \frac{R}{2 n}$ .
▸Lens cut in two along the axis: each half keeps the same $f$ (image dimmer). An equiconvex lens cut perpendicular to the axis: each (plano-convex) half has $2 f$ .
▸Displacement method (object–screen distance $D > 4 f$ , two lens positions x apart): $f = \frac{D ^{2} - x ^{2}}{4 D}$ , and $h = h_{1} h_{2}$ .

Comparative: lens types

	Convex	Concave
$f$ , $P$	$+$	$-$
Action	converging	diverging
Real image?	yes (object beyond $f$ )	never

🚫 Examiner Trap · Lenses

(1) Lens uses

1/ v - 1/ u

(

minus

); mirror uses

1/ v + 1/ u

(plus) — don't mix. (2) f depends on the

surrounding medium

: a glass lens is weaker in water and can even change converging

\leftrightarrow

diverging. (3) For lenses in contact powers ADD; with a gap subtract

d / f_{1} f_{2}

. (4) A diverging lens always gives a virtual, erect, diminished image.

Prism & Optical Instruments

Prism

A = r_{1} + r_{2}, δ = i_{1} + i_{2} - A; δ = (n - 1) A (small A)

A =

prism angle,

δ =

deviation,

r, i =

refraction/incidence angles

Minimum deviation

n = \frac{sin \frac{A + δ _{m}}{2}}{sin \frac{A}{2}}

δ_{m}

i_{1} = i_{2}

r_{1} = r_{2} = A /2

(symmetric passage)

A single ray passing through a prism of angle A at minimum deviation: it enters at angle i, travels parallel to the base inside, and leaves at angle e = i. The deviation delta is the angle between the extended incident ray and the emergent ray, with delta = i + e - A. — Minimum deviation: $i = e$ and the ray inside runs parallel to the base; $δ = i + e - A$ .

The δ–i curve (Experimental Skills)

▸As i increases, $δ$ first falls, reaches $δ_{m}$ at $i = e$ , then rises again (a U-shaped curve).
▸Each $δ > δ_{m}$ occurs at two angles of incidence, i and e (interchanging them gives the same $δ$ ).
▸Read $δ_{m}$ off the lowest point and use $n = \frac{sin \frac{A + δ _{m}}{2}}{sin \frac{A}{2}}$ .

Comparative: microscope vs telescope

Instrument	$M$ , image at $D$	M, image at $\infty$ (relaxed)
Simple microscope	$1 + \frac{D}{f}$	$\frac{D}{f}$
Compound micro.	$\frac{L}{f _{o}} (1 + \frac{D}{f _{e}})$	$\frac{L}{f _{o}} \cdot \frac{D}{f _{e}}$
Refracting telescope	$\frac{f _{o}}{f _{e}} (1 + \frac{f _{e}}{D})$	$\frac{f _{o}}{f _{e}}$ , length $f_{o} + f_{e}$
Reflecting telescope	—	$\frac{f _{o}}{f _{e}}$ with $f_{o} = \frac{R}{2}$ of the mirror

Instrument notes

▸ $D = 25$ cm (least distance of distinct vision); $L =$ tube length $\approx$ distance between the lenses.
▸Reflecting telescopes (Cassegrain) avoid chromatic aberration, and a large mirror is easier to support than a large lens.

🚫 Examiner Trap · Prism & instruments

(1)

δ

minimum

for symmetric passage (

i_{1} = i_{2}

); at any other angle

δ

is larger. (2) At

δ_{m}

the ray inside is parallel to the base and

r_{1} = r_{2} = A /2

; for a thin prism

δ = (n - 1) A

does not depend on i. (3)

Telescope

: large-f objective, small-f eyepiece (

M = f_{o} / f_{e}

);

microscope

: BOTH focal lengths small. (4) A telescope's M depends on the focal lengths, but its brightness (light gathered) and resolution depend on the objective's APERTURE (diameter) — a long focal length does not make it brighter.

Wave Optics — Huygens & Interference

Huygens & coherence

▸Every point on a wavefront is a source of secondary wavelets; their envelope is the new wavefront.
▸Interference needs two $coherent$ sources (constant phase difference, same frequency).
▸Huygens gives the laws: reflection $i = r$ ; refraction $\frac{sin i}{sin r} = \frac{v _{1}}{v _{2}} = \frac{n _{2}}{n _{1}}$ .
▸Same screen width, two wavelengths: $n_{1} λ_{1} = n_{2} λ_{2}$ (number of fringes $\propto 1/ λ$ ). White light: central fringe WHITE, coloured fringes either side (violet nearest).

Fringe width (YDSE)

β = \frac{λ D}{d}; y_{n}^{b r i g h t} = \frac{nλ D}{d}, y_{n}^{d a r k} = \frac{( 2 n - 1 ) λ D}{2 d}

d =

slit separation,

D =

screen distance; bright:

Δ x = nλ

, dark:

Δ x = (2 n - 1) λ /2

Young's double-slit setup with slit separation d, screen distance D and equally spaced bright fringes — Equally spaced fringes of width $β = λ D / d$ .

Intensity

I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ; \frac{I _{ma x}}{I _{min}} = \frac{( I _{1} + I _{2} ) ^{2}}{( I _{1} - I _{2} ) ^{2}}

ϕ =

phase difference; equal slits

\Rightarrow I_{ma x} = 4 I_{0}

I_{min} = 0

🚫 Examiner Trap · Interference / YDSE

(1) Sources must be

coherent

— two independent bulbs never interfere. (2) In a medium

β \to β / n

(the wavelength shrinks). (3) A thin sheet (

μ, t

) in one path shifts the pattern by

(μ - 1) t D / d

but

doesn’t change

β

. (4) Intensity adds as

(I_{1} \pm I_{2})^{2}

, not

I_{1} \pm I_{2}

— amplitudes add, not intensities.

Diffraction & Resolving Power

Single-slit minima

a sin θ = nλ (n = 1, 2, \dots)

a =

slit width; this gives

minima

(dark), the opposite of YDSE bright condition

Central maximum width

width = \frac{2 λ D}{a}; angular = \frac{2 λ}{a}

central max is

twice

as wide as the side maxima

Single-slit diffraction intensity pattern: a wide bright central maximum with weaker side maxima — Central max twice as wide as side maxima.

Resolving power (Rayleigh) — not in JEE Main 2026 syllabus

θ_{min} = \frac{1.22 λ}{D}

D =

aperture diameter; smaller

θ_{min} \Rightarrow

better resolution

Comparative: interference vs diffraction

	Interference	Diffraction
Sources	two coherent	one slit (parts)
Fringe spacing	equal	central widest
Intensities	all equal	fall off from centre

🚫 Examiner Trap · Diffraction & resolution

(1) For a single slit,

a sin θ = nλ

gives

minima

(in YDSE the same form gives maxima) — easy to confuse. (2) The central maximum is

twice

as wide and far brighter than side maxima. (3) Narrower slit

\Rightarrow

WIDER pattern (

\propto 1/ a

). (4) Diffraction sets the

resolution limit

of all instruments.

Polarisation

Polarisation: Confining the

E

vibrations of a transverse wave to one plane. Unpolarised light through one polaroid becomes plane-polarised with

half

the intensity (

I_{0} /2

Malus' law

I = I_{0} cos^{2} θ

θ =

angle between polariser and analyser axes;

I_{0} =

intensity after the polariser

Unpolarised light through a polariser then an analyser, transmitted intensity I0 cos squared theta — Polariser then analyser at angle $θ$ .

Brewster's law

tan θ_{p} = n

θ_{p}

reflected light is fully polarised; reflected

⊥

refracted (

θ_{p} + θ_{r} = 9 0^{\circ}

)

Key facts

▸Only $transverse$ waves polarise — proves light is transverse (sound can't).
▸Crossed polaroids ( $θ = 9 0^{\circ}$ ) block all light.
▸Uses: polaroid sunglasses, LCDs, 3-D glasses, stress analysis.

🚫 Examiner Trap · Polarisation

(1) First polaroid halves the intensity (

I_{0} /2

) for

unpolarised

input; Malus

I_{0} cos^{2} θ

applies

after

it. (2) Crossed polaroids (

9 0^{\circ}

) give zero — but a third at

4 5^{\circ}

in between lets some through. (3) Brewster:

tan θ_{p} = n

, and the reflected ray

⊥

refracted ray. (4) Only transverse waves polarise — a key proof that light is transverse.

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Frequently Asked Questions

What are the most important Optics formulas for JEE Main?

This Optics formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Reflection of light, Spherical mirrors, Mirror formula, Refraction of light, Total internal reflection and its applications — each shown with the key result and, where useful, a worked example.

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Blurt the Optics formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

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