NDA Physics · Formula sheet

Light and Optics formulas

11 formulas, 3 reference tables and 37 common traps for NDA Physics Light and Optics, grouped by subtopic.

Reflection and Mirrors

Spherical mirrors — pole, focus, centre, and R = 2f

Focal length and radius of curvature

f = \dfrac{R}{2}

$f$ focal length
$R$ radius of curvature (= PC)

Mirror formula and magnification

\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}, \qquad m = -\dfrac{v}{u}

$u$ object distance (from pole)
$v$ image distance (from pole)
$f$ focal length (−ve concave, +ve convex)
$m$ magnification (h'/h)

Common traps

Measure angles from the normal, not the surface

The single most common reflection error: a ray quoted as making angle θ with the mirror SURFACE has angle of incidence (90° − θ). NDA likes to state the surface angle and watch you forget to convert.

Virtual + erect + same-size — and only laterally inverted

Students often say a plane mirror 'inverts' the image and picture it upside down. It is ERECT. The only swap is left ↔ right (lateral inversion). Size is unchanged.

Half your height — distance does not matter

The minimum mirror height is always half the object height, no matter how far back you stand. Distractors tempt you with the full height or a distance-dependent answer.

R = 2f, so f = R/2 — not f = 2R

The focus is HALFWAY between the pole and the centre of curvature, so f is HALF of R. Flipping it to f = 2R is a classic slip.

Object at F gives the image at infinity, not between F and P

When an object sits between F and P the image IS virtual/erect/magnified — but it is the object at F (not the image) that goes to infinity. 'Image at infinity' is the false statement when the object is between F and P.

Only inside F does a concave mirror give a virtual image

Everywhere from infinity down to F the concave mirror gives a REAL, inverted image. The image only becomes virtual and erect once the object crosses inside the focus.

A convex mirror NEVER inverts

Because the image is always virtual and erect, a convex mirror can never produce an inverted image. Any option claiming an inverted convex-mirror image is the wrong statement.

Sign convention is the whole game

Almost every wrong numeric answer comes from a sign slip. Concave f is negative, convex f is positive, real distances in front of the mirror are negative. Write the signs down BEFORE substituting.

Magnification sign tells you real vs virtual

Negative m = real and inverted; positive m = virtual and erect. Don't read |m| alone and forget the sign — it carries the orientation.

Refraction, Speed of Light, and Total Internal Reflection

Learn this subtopic in the notes

Refraction and Snell's law

Snell's law of refraction

n_1 \sin\theta_1 = n_2 \sin\theta_2

$n_1, n_2$ refractive indices of the two media
$\theta_1$ angle of incidence (from the normal)
$\theta_2$ angle of refraction (from the normal)

Refractive index — n = c/v

Refractive index and speed

n = \dfrac{c}{v} \quad\Rightarrow\quad v = \dfrac{c}{n}, \qquad \dfrac{v_1}{v_2} = \dfrac{n_2}{n_1}

$n$ refractive index of the medium
$c$ speed of light in vacuum (≈ 3 × 10⁸ m/s)
$v$ speed of light in the medium

Total internal reflection and the critical angle

Critical angle

\sin\theta_c = \dfrac{1}{n}

$\theta_c$ critical angle (denser→rarer)
$n$ refractive index of the denser medium (vs air)

Common traps

Frequency is the invariant — not speed or wavelength

When asked what stays the same across a refraction boundary, the answer is always frequency. Speed and wavelength both change (in proportion); direction changes unless incidence is 0°.

Normal incidence still slows the light

At 0° incidence the ray does not bend, but it does change speed (and wavelength). 'No bending' is not the same as 'no change'.

Speed is the INVERSE of refractive index

Higher n means slower light, not faster. When comparing two media, flip the ratio: v₁/v₂ = n₂/n₁. The most-missed step is keeping the index ratio instead of inverting it.

Twinkling = refraction; blue sky / red sunset = scattering

Twinkling of stars and the early sunrise are REFRACTION effects. The blue colour of the sky and the red of sunset are SCATTERING (covered in Light Phenomena). Don't mix the two up — NDA tests both in the same paper.

TIR only goes denser → rarer

Total internal reflection cannot occur when light enters a denser medium. The light must be in the denser medium trying to escape into the rarer one. Miss this and the whole setup is wrong.

Both conditions, not just a big angle

A large angle of incidence alone is not enough — it must EXCEED the critical angle, and the direction must be denser-to-rarer. At exactly the critical angle you get grazing refraction, not TIR.

Mirage is TIR, not simple reflection or dispersion

A mirage is often miscalled 'reflection' or 'dispersion'. It is total internal reflection (preceded by gradual refraction through hot-air layers). The desert/hot-road illusion is the standard NDA cue for TIR.

Lenses and the Lens Formula

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Lens formula and the sign convention

Lens formula

\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}

$u$ object distance from optic centre (−ve for a real object)
$v$ image distance from optic centre
$f$ focal length (+ve convex, −ve concave)

Power of a lens — the dioptre

Power of a lens

P = \dfrac{1}{f\,(\text{in metres})}

$P$ power (dioptre, D)
$f$ focal length in METRES

Lens maker's equation

\dfrac{1}{f} = (n - 1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)

$n$ refractive index of the lens material
$R_1, R_2$ radii of curvature of the two faces (signed)
$f$ focal length

Lenses in contact — powers add

Combination of thin lenses in contact

P = P_1 + P_2, \qquad f = \dfrac{1}{P}

$P_1, P_2$ powers of the individual lenses (D)
$P$ power of the combination (D)
$f$ focal length of the combination (m)

Lens magnification and image formation

Lens magnification

m = \dfrac{h'}{h} = \dfrac{v}{u}

$m$ magnification
$v$ image distance
$u$ object distance

Common traps

A concave lens has no real-image setting

Unlike a concave MIRROR (which gives real images for most positions), a concave LENS gives a virtual, erect, diminished image for EVERY object position. Any claim that a concave lens makes real images is the wrong statement.

Lens uses 1/v − 1/u; mirror uses 1/v + 1/u

The two formulae look almost identical — a sign on the 1/u term is the only difference. Mixing them up flips your image distance. Memorise: lens is MINUS, mirror is PLUS.

Convert cm to metres before computing power

P = 1/f needs f in METRES. f = 25 cm gives P = 1/0.25 = 4 D, not 1/25 = 0.04 D. Forgetting the conversion is the standard power-question trap.

Sign the radii — convex faces are not both positive

For a double convex lens R₁ is positive but R₂ is negative, so 1/R₁ − 1/R₂ becomes 1/R₁ + 1/|R₂| — the terms ADD. Treating both as the same sign halves your answer.

Add powers, not focal lengths

For lenses in contact the POWERS add. Two +2 D lenses give +4 D ⟹ f = 0.25 m, NOT 1 m. Never add focal lengths directly.

Lens m = v/u (no minus); mirror m = −v/u

The magnification formula differs by a sign between lens and mirror. For a lens m = v/u; for a mirror m = −v/u. The sign convention then makes both give the right orientation — but use the correct one for the device.

Prisms and Dispersion

Learn this subtopic in the notes

Common traps

Deviation is refraction, not reflection

A prism bends light because it refracts at each face. Options blaming 'reflection' for the deviation or the colour spread are wrong — both are refraction effects.

Violet bends most because its speed in glass is LOWEST

The chain is: shortest wavelength → highest refractive index in glass → lowest speed in glass → greatest deviation. Distractors flip the speed ('highest speed') or swap red and violet. Red is the fast, least-bent one.

Primary rainbow = ONE internal reflection (the inner bow)

The primary bow has exactly one internal reflection and is the inner bow; two reflections make the fainter secondary (outer) bow. 'Refraction only' is wrong — reflection is always part of it.

The Human Eye and Optical Instruments

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Microscope and telescope

Telescope magnification (normal adjustment)

M = \dfrac{f_o}{f_e}

$f_o$ focal length of the objective
$f_e$ focal length of the eyepiece

Eye defects and their corrections

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.

Common traps

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.

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.

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.

Light Phenomena and the Electromagnetic Spectrum

Learn this subtopic in the notes

The electromagnetic spectrum

Wave / band	Typical wavelength	Use / note
Radio waves	> 1 m	Longest wavelength; broadcasting, communication
Microwaves	mm to cm	Radar, microwave ovens; LONGER wavelength than light
Infrared	~700 nm to 1 mm	Heat waves; absorbed strongly by water
Visible light	≈ 400–700 nm	The only band the eye detects
Ultraviolet (UV)	≈ 10–400 nm	Detects forgery in currency notes; higher energy than visibleQ
X-rays	≈ 0.01–10 nm (≈ 1 Å)	Smallest wavelength of the common four; medical imaging X-ray ≈ 1 nm ≈ 1 Å — the standard tested value. Smallest wavelength among radio/UV/visible/X-ray.
Gamma rays	< 0.01 nm	Highest energy of all

Memorise the ORDER (radio longest → gamma shortest) and the X-ray value (≈ 1 nm ≈ 1 Å). Sound is not on this list — it is mechanical, not electromagnetic.

Colours of light and the spectrum

Fact	Value
Primary colours of light	Red, Green, Blue (RGB) These ADD to white. Distinct from the primary pigments (paints).
Red + Green light gives	Yellow
Blue + Green light gives	Cyan
Red + Blue light gives	Magenta
Red + Green + Blue gives	White
First obtained sunlight's spectrum with a prism	Isaac NewtonQ
Order of colours in white light	VIBGYOR (Violet → Red)

The three primary colours of light are Red, Green, Blue; red + green = yellow; Newton first dispersed sunlight with a prism.

Common traps

Light speeds UP leaving a denser medium

Going from water/glass into air, light enters a rarer medium and speeds up. The trap statement claims it 'speeds down' — wrong. Also note c is 3 lakh KILOmetres per second, not metres per second.

Shorter wavelength = higher energy; UV beats visible

UV photons have MORE energy than visible photons (UV has the shorter wavelength). The trap statement 'UV energy is less than visible' is false. X-ray > UV > visible in energy.

EM waves are NOT elastic and DO travel in vacuum

EM waves need no medium (not elastic) and travel through vacuum. Their speed is 3 lakh KM/s. A statement saying they are elastic or move at '3 lakh metres per second' is wrong.

Sky/sunset colour = scattering; twinkling/early-sunrise = refraction

The blue sky and red sunset are SCATTERING. The twinkling of stars and seeing the Sun before it rises are atmospheric REFRACTION. NDA tests both in the same paper — keep them apart.

Primary colours of LIGHT are R, G, B — not R, Y, B

Red, Green, Blue are the primary colours of light (they add to white). Red-Yellow-Blue are pigment/paint primaries. The question almost always means light, so the answer is RGB.

Only polarization proves transverse nature

Refraction, diffraction and interference all happen for longitudinal waves (like sound) too, so they cannot prove light is transverse. Polarization is the unique discriminator.

The eye responds to the ELECTRIC field

Of an EM wave's two fields, it is the electric field that the eye (and detectors generally) respond to — not the magnetic field, and certainly not the infrared band.

Light and Optics formulas

Reflection and Mirrors

Spherical mirrors — pole, focus, centre, and R = 2f

Common traps

Refraction, Speed of Light, and Total Internal Reflection

Refraction and Snell's law

Refractive index — n = c/v

Total internal reflection and the critical angle

Common traps

Lenses and the Lens Formula

Lens formula and the sign convention

Power of a lens — the dioptre

Lenses in contact — powers add

Lens magnification and image formation

Common traps

Prisms and Dispersion

Common traps

The Human Eye and Optical Instruments

Microscope and telescope

Eye defects and their corrections

Common traps

Light Phenomena and the Electromagnetic Spectrum

The electromagnetic spectrum

Colours of light and the spectrum

Common traps

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