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Chapter 01 · Part IV · Optics
Revised on ____________________
Chapter 01 · Ray Optics

Assign every sign before you write a single equation

2 sheets
2 diagrams
30 results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

I

The convention, and mirrors

SIGNS FIRST, ALGEBRA SECOND
I.Origin  the pole; light travels left to right distances against the light are negative
II.Real object  u < 0 always, for both mirrors and lenses
III.Focal length  concave mirror f < 0, convex f > 0
IV.Mirror equation  1v + 1u = 1f
V.Focus  f = R2
VI.Magnification  m = − vu the minus sign is the mirror's
VII.Nature from the sign  v < 0 real, v > 0 virtual never guess it in advance
VIII.Longitudinal  mlong = − m² for a short object along the axis
P (pole / optical centre)incident lightdistances +distances −height +height −
II

Refraction

TIR NEEDS BOTH CONDITIONS
I.Refractive index  n = cv = λvacλmed frequency never changes
II.Snell's law  n1 sin θ1 = n2 sin θ2
III.Apparent depth  dapp = nobservernobject dreal
IV.Shift through a slab  d = t ( 1 − 1n ) no deviation, only a shift
V.Critical angle  sin θc = n2n1 denser → rarer only
VI.Refraction at a surface  n2v − n1u = n2 − n1R
III

Lenses

m = + v/u — THE OPPOSITE OF A MIRROR
I.Lens equation  1v − 1u = 1f
II.Magnification  m = vu
III.Lens-maker  1f = (n − 1) ( 1R1 − 1R2 )
IV.Power  P = 1f (m) dioptres
V.In contact  P = P1 + P2
VI.Separated by d  P = P1 + P2 − d P1 P2
VII.Silvered lens  P = 2Plens + Pmirror light crosses the lens twice
VIII.In a medium  1f = ( nlensnmed − 1 ) ( 1R1 − 1R2 )
2FFFOIreal, invertedconvergingFOI′virtual, erectdiverging
IV

Prisms and instruments

MINIMUM DEVIATION IS SYMMETRIC
I.Deviation  δ = i1 + i2 − A
II.At minimum  n = sin((A + δm)/2)sin(A/2) only when i₁ = i₂
III.Thin prism  δ = (n − 1) A
IV.Dispersive power  ω = nV − nRnY − 1
V.Simple microscope  M = 1 + Df D = 25 cm
VI.Compound microscope  M = vouo ( 1 + Dfe )
VII.Telescope  M = fofe tube length fo + fe
VIII.Eye defects  myopia: concave; hypermetropia: convex
V

Where the marks go

FOUR ERRORS, EVERY YEAR
Where marks are lost in this chapter
1Plugging in magnitudes and fixing the sign at the end. Assign every sign from the data and let the algebra answer.
2Carrying the mirror's m = −v/u into a lens problem. For a lens m = + v/u — memorise the pair together.
3Inverting the apparent-depth ratio. It is (observer-side index) ÷ (object-side index), always.
4Applying a critical angle going rarer → denser. Total internal reflection needs n1 > n2 and θ > θc.