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Formula Sheets / Physics

Chapter 26

Ray Optics

Revise with flashcards Download this chapter (PDF) All Physics formulas (PDF)

Reflection and mirrors Refraction and total internal reflection Lenses Prism and dispersion Optical instruments

Reflection and mirrors

Mirror formula
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f},$ $f = \frac{R}{2},$ $m = - \frac{v}{u}$
Use the sign convention: distances measured from the pole, along the incident light positive.
Plane mirrors
images of an object between mirrors at angle $θ : n = \frac{36 0 ^{\circ}}{θ} - 1 ($ if $36 0^{\circ} / θ$ is even $)$
Rotating mirror
mirror turns by $θ \Rightarrow$ reflected ray turns by $2 θ$

Refraction and total internal reflection

Snell's law
$n_{1} sin i = n_{2} sin r,$ $n = \frac{c}{v}$
Apparent depth
$d^{'} = \frac{d}{n};$ shift $= t (1 - \frac{1}{n})$
Critical angle
$sin C = \frac{1}{n} ($ denser to rarer, into air $)$
Spherical surface
$\frac{n _{2}}{v} - \frac{n _{1}}{u} = \frac{n _{2} - n _{1}}{R}$

Lenses

Lens formula
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f},$ $m = \frac{v}{u}$
Lens maker's formula
$\frac{1}{f} = (n - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$
Power and combinations
$P = \frac{1}{f}$ (in m) $;$ $P = P_{1} + P_{2}$ (in contact) $;$ $\frac{1}{F} = \frac{1}{f _{1}} + \frac{1}{f _{2}} - \frac{d}{f _{1} f _{2}}$
Displacement method
$f = \frac{D ^{2} - x ^{2}}{4 D}$

Prism and dispersion

$A = r_{1} + r_{2},$ $δ = i + e - A$
Minimum deviation
$n = \frac{sin \frac{A + δ _{m}}{2}}{sin \frac{A}{2}}$
Thin prism
$δ = (n - 1) A$
Dispersion
$θ = (n_{v} - n_{r}) A,$ $ω = \frac{n _{v} - n _{r}}{n _{y} - 1}$
Achromatic / no deviation
$\frac{ω _{1}}{f _{1}} + \frac{ω _{2}}{f _{2}} = 0;$ $(n_{1} - 1) A_{1} = (n_{2} - 1) A_{2}$

Optical instruments

Simple microscope
$m = 1 + \frac{D}{f}$ (image at $D),$ $m = \frac{D}{f}$ (at infinity)
Compound microscope
$m = \frac{v _{o}}{u _{o}} (1 + \frac{D}{f _{e}});$ at infinity $m \approx \frac{L}{f _{o}} \cdot \frac{D}{f _{e}}$
Telescope
$m = \frac{f _{o}}{f _{e}}$ (normal adjustment) $,$ $L = f_{o} + f_{e}$

Electromagnetic Waves Wave Optics