IMAT Physics · Formula sheet

Optics formulas

4 formulas, 3 reference tables and 8 common traps for IMAT Physics Optics, grouped by subtopic.

Mirrors, Refraction and Total Internal Reflection

Refraction, refractive index and Snell's law

Refractive index and Snell's law

n = \frac{c}{v} \qquad n_1 \sin\theta_1 = n_2 \sin\theta_2

$n$ refractive index (no unit)
$c$ speed of light in a vacuum, $3.00 \times 10^8$ m/s
$v$ speed of light in the medium
$\theta_1,\ \theta_2$ angles of incidence and refraction, from the normal

Total internal reflection and the critical angle

Critical angle

\sin C = \frac{n_2}{n_1} \qquad \sin C = \frac{1}{n} \ \text{(into air)}

$C$ critical angle, measured from the normal
$n_1$ refractive index of the denser medium the light starts in
$n_2$ refractive index of the less dense medium

The laws of reflection and the plane mirror image

Property	Plane mirror image
Position	As far behind the mirror as the object is in front
Size	Same size as the object
Orientation	Upright, but left and right are swapped (laterally inverted)
Type	Virtual: it cannot be projected on a screen
Full-length mirror	Needs to be only half your height

Concave and convex mirrors: rays and images

Mirror and object position	Image	Use
Concave, object beyond $C$	Real, inverted, smaller, between $F$ and $C$	Telescope mirrors collecting light from far away
Concave, object at $C$	Real, inverted, same size, at $C$	Checking the radius of curvature in a lab
Concave, object between $C$ and $F$	Real, inverted, larger, beyond $C$	Projecting an enlarged image onto a screen
Concave, object at $F$	No image: the reflected rays are parallel	Torch and headlamp reflectors, with the bulb at $F$
Concave, object between $F$ and the mirror	Virtual, upright, larger, behind the mirror	Make-up and dentists' mirrors
Convex, any position	Virtual, upright, smaller, behind the mirror	Car wing mirrors and shop security mirrors

Common traps

Angles in optics are measured from the normal

The angle of incidence is between the ray and the normal, not the surface. A ray at 30° to a mirror has an angle of incidence of 60°. The same rule applies in refraction.

A concave mirror does not always give a real, inverted image

With the object between the focal point and the mirror, a concave mirror gives a virtual, upright, magnified image. Its image is also not always larger: an object far beyond

C

gives a smaller one. Statements with "always" about concave images are usually false.

Refraction changes the wavelength, not the frequency

In glass, light slows down and its wavelength shrinks by the factor

n

, but its frequency, and so its colour, is unchanged. Options claiming the colour or frequency changes inside the glass are wrong.

Total internal reflection only happens going into a less dense medium

TIR needs light travelling from a higher refractive index to a lower one, at more than the critical angle. Light entering glass from air always gets in (some is partly reflected), whatever the angle.

Lenses, Power and Vision Defects

Learn this subtopic in the notes

Converging and diverging lenses and the thin lens equation

Thin lens equation and magnification

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \qquad m = -\frac{d_i}{d_o} = \frac{h_i}{h_o}

$f$ focal length: positive for converging, negative for diverging
$d_o$ distance of the object from the lens
$d_i$ distance of the image: positive real, negative virtual
$h_o,\ h_i$ heights of object and image

Lens power in dioptres

Power of a lens

P = \frac{1}{f} \qquad P_{\text{total}} = P_1 + P_2

$P$ power, in dioptres (D)
$f$ focal length, in metres

The human eye, short sight and long sight

Part or defect	What it does or what goes wrong	Note or correction
Cornea	Does most of the focusing, at the curved air to cornea surface	Its power is fixed
Lens and ciliary muscles	Fine focusing: the muscles change the lens's shape (accommodation)	The lens becomes fatter for near objects
Iris and pupil	The iris changes the size of the pupil to control how much light enters	The pupil narrows in bright light
Retina	Light-sensitive layer where a real, inverted image forms	The brain interprets the image upright
Myopia (short sight)	Eyeball too long or lens too strong: image in front of the retina	Diverging lens, negative power
Hypermetropia (long sight)	Eyeball too short or lens too weak: image behind the retina	Converging lens, positive power
Presbyopia	With age the lens stiffens and cannot accommodate for near objects	Converging reading glasses

Common traps

A converging lens does not always give a real image

With the object closer to a converging lens than its focal point, the image is virtual, upright and magnified, on the same side as the object. That is how a magnifying glass works.

Power needs the focal length in metres

A lens with

f = 20\ \text{cm}

has

P = 1/0.20 = 5\ \text{D}

. Using 20 instead of 0.20 gives 0.05 D, a hundred times too small, and that slip is a favourite wrong option.

Short sight needs a diverging lens

A myopic eye focuses too strongly, so the correction must weaken it: a diverging lens with negative power. Long sight is the opposite and needs a converging lens. Swapping the two is the usual wrong option.

The cornea, not the lens, does most of the focusing

The biggest change of refractive index is between air and the cornea, so most of the bending happens there. The lens only fine-tunes the focus by changing shape.

Optics formulas

Mirrors, Refraction and Total Internal Reflection

Refraction, refractive index and Snell's law

Total internal reflection and the critical angle

The laws of reflection and the plane mirror image

Concave and convex mirrors: rays and images

Common traps

Lenses, Power and Vision Defects

Converging and diverging lenses and the thin lens equation

Lens power in dioptres

The human eye, short sight and long sight

Common traps

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