REFLECTION + PLANE MIRRORS
Law of Reflection
θᵢ = θᵣ — angles from the NORMAL
Plane mirror
Virtual, upright, same size
Image dist.
= object distance (behind mirror)
Laterally inv.
Left ↔ right swapped
Specular refl.
Smooth surface → clear image
Diffuse refl.
Rough surface → scattered rays
INDEX OF REFRACTION
n = c / v c = 3×10&sup8; m/s
Denser medium
higher n → slower light
| Medium | n |
|---|
| Air | 1.00 |
| Water | 1.33 |
| Glass | 1.50 |
| Diamond | 2.42 |
SNELL'S LAW + TOTAL INTERNAL REFLECTION
Snell's Law: n₁ sinθ₁ = n₂ sinθ₂
Angles from
the NORMAL, not the surface
Into denser
bends TOWARD normal (θ decreases)
Into less dense
bends AWAY from normal (θ increases)
TOTAL INTERNAL REFLECTION
Only when going dense → less dense
Critical angle
sinθ₃ = n₂ / n₁
TIR condition
θ > θ₃ (and dense→less dense)
TIR cannot occur going from air into glass — only from glass (dense) into air (less dense).
APPLICATIONS OF TIR
- Optical fibres (data transmission)
- Diamonds (n=2.42, θ₃=24.4°, sparkle)
- Mirages (hot air bends light)
- Endoscopes (medical imaging)
MIRRORS + LENSES EQUATIONS
Mirror equation: 1/f = 1/d᷹ + 1/dᵢ
Same form for thin lenses!
Concave f
f > 0 (converging)
Convex f
f < 0 (diverging)
Real image dᵢ
dᵢ > 0 (in front of mirror)
Virtual dᵢ
dᵢ < 0 (behind mirror)
R = 2f
radius = twice focal length
THIN LENS EQUATION
1/f = 1/d᷹ + 1/dᵢ (identical form)
Converging f
f > 0 (convex lens)
Diverging f
f < 0 (concave lens)
Real image
dᵢ > 0 (opposite side)
Virtual image
dᵢ < 0 (same side as object)
MAGNIFICATION (BOTH)
Formula
m = −dᵢ / d᷹ = hᵢ / h᷹
RAY DIAGRAMS — CONVERGING LENS
Draw any 2 of the 3 rays. Intersection = image.
- Ray 1: Parallel to axis → through far focal point F′
- Ray 2: Through optical centre → straight through (no bend)
- Ray 3: Through near focal point F → parallel to axis
RAY DIAGRAMS — CONCAVE MIRROR
- Ray 1: Parallel to axis → reflects through F
- Ray 2: Through F → reflects parallel to axis
- Ray 3: Through C (=2F) → reflects straight back
COMMON MISTAKES
- Angles always from the NORMAL, not the surface
- n = c/v (not v/c) — n is always ≥ 1
- Mirror and lens equations are identical in form
- Negative m → image is inverted (not necessarily smaller)
- Critical angle only exists for dense → less dense
- TIR cannot happen going from air into glass
IMAGE SUMMARY — CONVERGING LENS
| Object at | Image | Orient. |
|---|
| Beyond 2F | Real, reduced | Inv. |
| At 2F | Real, same size | Inv. |
| F to 2F | Real, enlarged | Inv. |
| At F | No image (∞) | — |
| Inside F | Virtual, enlarged | Upright |