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Light and Optics formulas

3 formulas, 5 reference tables and 18 common traps for SPI Physics Light and Optics, grouped by subtopic.

Light and Reflection

The laws of reflection

Law of reflection

\angle r = \angle i \qquad \angle i = 90^\circ - (\text{angle between the ray and the mirror})

What light is

Fact	Value
Kind of wave	Electromagnetic
Transverse or longitudinal	Transverse Sound is the longitudinal one; light is not.
Needs a medium	No, it travels through a vacuum
Speed in a vacuum	$3 \times 10^8$ m/s
Path in one medium	Straight lines, so opaque objects cast shadows
Ray	One straight line along which light travels
Beam	A bundle of rays

Radio waves, X-rays and light are all electromagnetic waves; they differ only in wavelength.

Plane, concave and convex mirrors and their uses

Mirror	Image	Uses
Plane	Virtual, erect, same size	Looking glass, periscope
Concave, object far away	Real and inverted	Torch and headlight reflectors, solar cookers
Concave, object very close	Virtual, erect, enlarged	Shaving and make-up mirrors, a dentist's mirror
Convex	Always virtual, erect, diminished	Rear-view and side-view mirrors of vehicles, shop security mirrors Widest field of view of the three.

A torch or headlight puts its bulb at the focus of a concave mirror to send out a parallel beam.

Common traps

Calling light a radio wave

Radio waves and light belong to the same electromagnetic family, but light is not a radio wave. The family name is 'electromagnetic waves'.

Calling light longitudinal

Light is transverse: its fields vibrate across its direction of travel. A longitudinal wave, like sound, vibrates along it.

Measuring from the mirror

A ray at

30^\circ

to the mirror's surface has an angle of incidence of

60^\circ

, because the angle is taken from the normal.

Thinking the law fails for curved mirrors

The angle of reflection equals the angle of incidence for every mirror, every time. On a curved mirror, use the normal at the point where the ray strikes.

Choosing a plane mirror for the rear view

A plane mirror shows only an area as big as itself. A convex mirror shows a much wider area, which is why vehicles use it.

Thinking a concave mirror always gives a real image

With the object between the focus and the mirror, a concave mirror gives a virtual, erect, enlarged image. That is how a shaving mirror works.

Refraction and Lenses

Learn this subtopic in the notes

Refractive index and the bending of light

Refractive index

n = \frac{c}{v} \qquad n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2}

$c$ speed of light in a vacuum, 3 × 10⁸ m/s
$v$ speed of light in the medium
n₂₁refractive index of medium 2 with respect to medium 1

Convex and concave lenses, the lens formula and power

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{m})}

Common traps

Higher refractive index means faster light

It is the reverse:

v = \frac{c}{n}

, so the medium with the larger n is the one where light is slower.

Thinking water makes a lens stronger

A glass lens bends light less in water than in air, because glass and water differ less in refractive index. Its focal length grows, so its power falls.

Picking the pair with the largest indices

The bending depends on how much the two indices DIFFER. Going between n = 2.6 and n = 2.7 changes light less than going between 1.3 and 2.0.

Using centimetres in the power formula

Power needs the focal length in metres. A 20 cm lens has power

\frac{1}{0.2} = 5

D, not

\frac{1}{20}

Forgetting the sign of a concave lens

A concave lens has a negative focal length, so its power is negative. A lens of power

-2.5

D is concave.

Putting the same-size image at F

An object at F sends its image to infinity. The same-size image comes from an object at 2F, with the image at 2F.

The Eye, Dispersion and Instruments

Learn this subtopic in the notes

Defects of vision and the lens that corrects each

Defect	What goes wrong	Corrected with
Myopia (short sight)	Far objects blur; the image forms in front of the retina	Concave lens
Hypermetropia (long sight)	Near objects blur; the image forms behind the retina	Convex lens
Presbyopia	Old age: the ciliary muscles weaken, so near and often far vision both suffer	Bifocal lens
Astigmatism	The cornea is curved unequally, so lines in one direction blur	Cylindrical lens Not convex or concave: a cylindrical lens.
Cataract	The eye lens turns cloudy	Surgery to replace the lens

Short sight takes a concave lens, long sight a convex one: the opposite of what the names might suggest.

Dispersion, the spectrum and atmospheric refraction

Event	Cause
A prism forms a spectrum	Dispersion: each colour refracts by a different amount
A rainbow	Dispersion and reflection inside raindrops; seen with the Sun behind you
Stars twinkle	Atmospheric refraction that keeps changing
Planets do not twinkle	They are close, so they look like discs, and the changes average out
The Sun is seen about 2 minutes before it rises	Atmospheric refraction bends its light over the horizon
The sky is blue	Air scatters blue light much more than red
Danger signals are red	Red is scattered least, so it is seen from far away

Splitting is dispersion; bending is refraction; spreading by tiny particles is scattering.

Optical instruments and what each is for

Instrument	Used for
Telescope	Distant objects such as stars and planets
Binoculars	Distant objects, with both eyes
Microscope	Very small objects close by, such as cells
Periscope	Seeing over an obstacle, using two plane mirrors
Kaleidoscope	Repeating patterns from plane mirrors
Spectroscope	Splitting light into its spectrum to study it
Chronometer	Measuring time very accurately Not an optical instrument at all.

The suffix tells the job: tele means far, micro means small, peri means around.

Common traps

Concave lens for long sight

Long sight (hypermetropia) puts the image behind the retina and needs a converging, convex lens. The concave lens is for short sight.

Bifocal for astigmatism

A bifocal lens is for presbyopia. Astigmatism comes from an unevenly curved cornea and needs a cylindrical lens.

Calling the splitting 'refraction'

Each colour is refracted, but the splitting of white light into colours has its own name: dispersion.

Violet bends least

Red bends least and has the smallest refractive index in glass; violet bends most.

Planets twinkle too

Planets are near enough to look like small discs, so the changes from many points cancel and they shine steadily.

Telescope and microscope swapped

A telescope is for far objects and a microscope for tiny near ones. 'Tele' means far, as in telephone.

Light and Optics formulas

Light and Reflection

The laws of reflection

What light is

Plane, concave and convex mirrors and their uses

Common traps

Refraction and Lenses

Refractive index and the bending of light

Convex and concave lenses, the lens formula and power

Common traps

The Eye, Dispersion and Instruments

Defects of vision and the lens that corrects each

Dispersion, the spectrum and atmospheric refraction

Optical instruments and what each is for

Common traps

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