CDS Physics · Formula sheet

Light and Optics formulas

5 formulas, 7 reference tables and 22 common traps for CDS Physics Light and Optics, grouped by subtopic.

Reflection and Mirrors

Laws of reflection and the plane mirror

Law of reflection and the deviation by a plane mirror

i = r \qquad \delta = 180^\circ - 2i

$i$ angle of incidence, from the normal
$r$ angle of reflection, from the normal
$\delta$ angle through which the ray is turned

Concave and convex mirrors

Focal length, mirror formula and magnification

f = \frac{R}{2} \qquad \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \qquad m = -\frac{v}{u}

$R$ radius of curvature
$f$ focal length (negative for a concave mirror)
$u, v$ object and image distances from the pole
$m$ magnification; negative means inverted

Light travels in straight lines: shadows

Situation	What you see
Light in a uniform transparent medium	A straight pathQ CDS 2016 (II): light keeps a straight line only in a homogeneous, transparent medium.
Point source and an opaque object	Umbra only: a sharp shadow
Extended source and an opaque object	Umbra with a penumbra round it: a blurred edge
Pinhole camera	Inverted real image
Standing in the Moon's umbra	Total solar eclipse

Common traps

Straight lines need a uniform medium

Light goes straight only where the refractive index is the same everywhere. Slabs of different refractive index, or a medium whose index changes from place to place, bend the ray.

Angles are measured from the normal

If a stem gives the angle with the mirror surface, subtract it from 90° first. A ray at 30° to the surface has

i = 60^\circ

, and its deviation is 60°, not 120°.

A plane mirror's image is virtual

The image is erect, the same size and laterally inverted, but it is never real: the rays only seem to come from behind the mirror.

The focus is at half the radius

For a spherical mirror

f = R/2

. An object at a distance equal to

R/2

is at the focus, so its image is at infinity, not at the centre of curvature.

Erect at every distance means plane or convex

A concave mirror gives an erect image only when the object is inside its focus. If the image stays erect wherever you stand, the mirror is plane or convex, and the stem cannot tell which.

Refraction and Lenses

Learn this subtopic in the notes

Refraction and the refractive index

Refractive index and Snell's law

n = \frac{c}{v} \qquad n_1 \sin i = n_2 \sin r

$n$ refractive index of the medium
$c$ speed of light in vacuum, about $3 \times 10^{8}$ m/s
$v$ speed of light in the medium
$i, r$ angles of incidence and refraction, from the normal

Total internal reflection

Critical angle

\sin C = \frac{1}{n}

$C$ critical angle, inside the denser medium
$n$ refractive index of the denser medium relative to the rarer one

Lens formula, magnification and power

\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \qquad m = \frac{v}{u} \qquad P = \frac{1}{f\,(\text{in m})}

$u, v$ object and image distances from the lens
$f$ focal length (positive for convex)
$m$ magnification
$P$ power, in dioptres

Images formed by a convex lens

Object position	Image (convex lens)
Beyond 2F	Between F and 2F; real, inverted, smaller
At 2F	At 2F; real, inverted, same size
Between F and 2F	Beyond 2F; real, inverted, enlargedQ CDS 2020 (II): an object 40 cm from a lens of focal length 25 cm gives an inverted, magnified image.
At F	At infinityQ CDS 2022 (II): an object at the focus of a convex lens has its image at infinity.
Between F and the lens	Same side; virtual, erect, enlarged

Common traps

Refractive index is c over v, not v over c

n = c/v

is always greater than 1. Writing

v/c

gives a number below 1, which no material has. To find the speed in a medium, divide

c

n

; never multiply.

Slower means towards the normal

Going into a denser medium, light slows down and bends towards the normal. The two halves always go together: an option pairing 'slows down' with 'away from the normal' is wrong.

Higher refractive index, smaller critical angle

From

\sin C = 1/n

, a larger

n

gives a smaller

C

. Diamond (24°) traps light more easily than glass (42°), which is why it sparkles.

Enlarged and real needs F to 2F

A convex lens gives a real, enlarged image only with the object between F and 2F. At 2F the image is the same size; beyond 2F it is smaller; inside F it is enlarged but virtual.

Object at the focus: no image at a finite distance

Light from the focus leaves the lens parallel, so the image is at infinity. It is not at the focus on the other side, which is where light from infinity goes.

Focal length in metres before taking the reciprocal

P = 1/f

needs

f

in metres. A 25 cm lens has

P = 1/0.25 = 4

D, not 1/25 = 0.04 D. Most wrong options are off by a factor of 100.

Bending power goes by size, not sign

A +2.5 D lens bends light more than a −2.0 D lens, and a −3 D lens more than a +2 D lens. Compare the sizes of the powers; the sign only says converging or diverging.

Positive magnification means virtual

For a lens

m = v/u

. A positive

m

means an erect, virtual image, and

|m| > 1

means it is enlarged. A real image from a single lens always has a negative

m

Dispersion, Scattering and the Spectrum

Learn this subtopic in the notes

The electromagnetic spectrum

Radiation	Wavelength and a use
Radio waves and microwaves	Longest, above about 1 mm; broadcasting and satellite communicationQ CDS 2020 (I): satellite communication uses radio waves.
Infrared	About 1 mm down to 700 nm; heat, remote controls
Visible light	About 700 nm to 400 nm; the only part the eye seesQ CDS 2018 (II): the visible portion of the electromagnetic spectrum is light.
Ultraviolet	Below 400 nm; sterilising, causes sunburnQ CDS 2020 (I): of radio, visible, infrared and ultraviolet, ultraviolet has the shortest wavelength.
X-rays	Much shorter; imaging bones
Gamma rays	Shortest; from radioactive nuclei

Dispersion by a prism and the rainbow

Step inside a raindrop	What happens to the light
Light enters the drop	Refraction and dispersion into colours
Light reaches the back of the drop	One internal reflection (primary rainbow)Q CDS 2024 (II): a rainbow needs both refraction and internal reflection of sunlight.
Light leaves the drop	Refraction again, spreading the colours further
Secondary rainbow	Two internal reflections; colours in reverse order

Scattering and atmospheric refraction

What you see	Cause
Blue sky	Scattering of short-wavelength light by air molecules
Reddish Sun near the horizon	Scattering removes blue over the long path through air
Red danger lights	Red is scattered least
Twinkling of stars	Atmospheric refractionQ Asked twice: CDS 2022 (I) and 2025 (II). The answer is refraction, never reflection, interference or diffraction.
Sun seen 2 minutes before sunrise	Atmospheric refraction

Common traps

Shorter wavelength means more energy, not less

Energy per photon rises as the wavelength falls. Ultraviolet has a shorter wavelength than visible light and so more photon energy; infrared has a longer wavelength and less.

Microwaves are part of the radio band

Satellite links use microwave frequencies, which lie within the radio-wave region of the spectrum. Infrared, ultraviolet and visible light are not used for satellite communication.

A rainbow needs refraction and reflection together

Refraction alone gives no rainbow, and nor does reflection alone. Light is refracted in, reflected once inside, and refracted out. An option naming only one of these is incomplete.

Violet bends most, red least

Glass has its highest refractive index for violet light, so violet is deviated the most. Red, with the longest wavelength, is deviated the least.

Twinkling is refraction; the red Sun is scattering

Two sky questions, two different causes. Stars twinkle because of atmospheric refraction. The Sun looks red at the horizon because of scattering. Dispersion and reflection are distractors for both.

Blue is scattered most, red least

Scattering by air molecules grows sharply as the wavelength falls. That one rule gives the blue sky, the red sunset and the red danger light.

The Eye and Optical Instruments

Learn this subtopic in the notes

Defects of vision and their correction

Defect	Cause and correction
Myopia (near-sightedness)	Lens too curved or eye-ball too long; concave lensQ CDS 2025 (I): myopia is also called near-sightedness.
Hypermetropia (far-sightedness)	Focal length too long or eye-ball too short; convex lens
Presbyopia	Ageing weakens accommodation; bifocal or progressive lensesQ CDS 2024 (II): presbyopia comes with age and is corrected with bifocal or progressive lenses; it does not affect colour vision.
Cataract	Cloudy eye lens; surgery

Microscopes and telescopes

Instrument	Lenses used
Simple microscope	One converging (convex) lensQ CDS 2025 (I): a simple microscope uses a converging lens.
Compound microscope	Convex objective of very short focal length, convex eyepiece
Astronomical telescope	Convex objective of long focal length, convex eyepiece of short focal length
Galilean telescope	Convex objective, concave eyepiece

Common traps

Near-sighted means it is the far objects that blur

A near-sighted (myopic) person sees near objects clearly and distant ones blurred. Far-sighted is the opposite. The name says what the person can still see.

Myopia: lens too strong or eye-ball too long

Myopia comes from too much bending (an over-curved lens, a short focal length) or an elongated eye-ball. A small eye-ball or a long focal length gives hypermetropia instead.

Telescope objective long, microscope objective short

A telescope objective has a long focal length to gather light from far away. A microscope objective has a very short one to magnify a near object. Both instruments use convex lenses for both parts, except the Galilean telescope.

Light and Optics formulas

Reflection and Mirrors

Laws of reflection and the plane mirror

Concave and convex mirrors

Light travels in straight lines: shadows

Common traps

Refraction and Lenses

Refraction and the refractive index

Total internal reflection

Images formed by a convex lens

Common traps

Dispersion, Scattering and the Spectrum

The electromagnetic spectrum

Dispersion by a prism and the rainbow

Scattering and atmospheric refraction

Common traps

The Eye and Optical Instruments

Defects of vision and their correction

Microscopes and telescopes

Common traps

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