Analyze image formation using curved mirrors (concave and convex). For three different object positions, find the following properties using two methods (graphical ray diagram and algebraic calculation):

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Physics
Prelab 14 – Mirror Ray Diagrams Explained

Prelab 14 – Mirror Ray Diagrams

Question:
Analyze image formation using curved mirrors (concave and convex). For three different object positions, find the following properties using two methods (graphical ray diagram and algebraic calculation):
  • Image location
  • Image height and magnification
  • Image type: Real or Virtual
  • Image orientation: Upright or Inverted
  • Image size: Enlarged or Reduced
Constants:
  • Object height = 2 cm
  • Focal length = ±6 cm (positive for concave, negative for convex)
Scenarios:
  1. Concave mirror, object 10 cm away
  2. Concave mirror, object 4 cm away
  3. Convex mirror, object 4 cm away

🔍 Method 1 – Ray Diagram (Graphical)

Steps:
  1. Draw a horizontal principal axis.
  2. Sketch the mirror and mark focal point (F) and center of curvature (C).
  3. Place the object upright (2 cm) at correct distance.
  4. Draw rays:
    • Ray 1: Parallel to axis → reflects through F
    • Ray 2: Through F → reflects parallel
    • Ray 3: Through C → reflects back
  5. Where rays intersect = image location
  6. Measure height to determine size and orientation

🧮 Method 2 – Algebra (Mirror and Magnification Equations)

Equations:
Mirror equation: 1/f = 1/do + 1/di
Magnification: M = -di/do = hi/ho

📘 Solutions for Each Scenario:

Scenario 1: Concave Mirror, Object at 10 cm
f = +6 cm, do = 10 cm
1/f = 1/do + 1/di → 1/6 = 1/10 + 1/di → di = 15 cm
M = -15/10 = -1.5 → hi = -3 cm
  • Image Location: 15 cm (in front of mirror)
  • Image Height: –3 cm
  • Type: Real
  • Orientation: Inverted
  • Size: Enlarged
Scenario 2: Concave Mirror, Object at 4 cm
f = +6 cm, do = 4 cm
1/f = 1/do + 1/di → 1/6 = 1/4 + 1/di → di = -12 cm
M = -(-12)/4 = +3 → hi = 6 cm
  • Image Location: –12 cm (behind mirror)
  • Image Height: +6 cm
  • Type: Virtual
  • Orientation: Upright
  • Size: Enlarged
Scenario 3: Convex Mirror, Object at 4 cm
f = –6 cm, do = 4 cm
1/f = 1/do + 1/di → 1/–6 = 1/4 + 1/di → di ≈ –2.4 cm
M = –(–2.4)/4 = +0.6 → hi ≈ 1.2 cm
  • Image Location: –2.4 cm (behind mirror)
  • Image Height: +1.2 cm
  • Type: Virtual
  • Orientation: Upright
  • Size: Reduced
✅ Final Summary:
Scenario 1: Real, Inverted, Enlarged (15 cm, –3 cm)
Scenario 2: Virtual, Upright, Enlarged (–12 cm, +6 cm)
Scenario 3: Virtual, Upright, Reduced (–2.4 cm, +1.2 cm)

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