Chapter 7 — ICSE-style interactive simulations with animated ray diagrams matching your textbook. Covers all 6 concave mirror cases, convex mirror, plane mirrors, and a 15-question quiz.
Part 1 — Plane Mirrors
✦ Laws of Reflection
✦ Regular vs Diffuse
✦ Image properties
✦ Lateral Inversion
✦ n = (360°/θ) − 1
Part 2 — Spherical
✦ Concave & Convex
✦ Terms: P, C, F, R, f
✦ 4 Ray-diagram rules
✦ 6 Cases (Concave)
✦ Convex mirror images
Part 3 — Formulas
✦ 1/v + 1/u = 1/f
✦ m = −v/u
✦ Cartesian Convention
✦ Uses of mirrors
✦ Concave vs Convex
⚠ Exam Alert — Always draw arrows on rays. Use dotted lines for virtual images and extensions behind the mirror. Ensure PF = FC. Case 6 (object between F and P) is the most frequently asked diagram in ICSE exams.
Quick Formulas
f = R/2
Focal length = half radius of curvature
1/v + 1/u = 1/f
Mirror Formula
m = −v/u = hᵢ/h₀
Magnification
n = (360°/θ)−1
Number of images by two mirrors
Memory Aids
∠i = ∠r — angles from the normal
Concave = Converging (curves inward)
Convex = Diverging (bulges outward)
Concave f is negative (−)
Convex f is positive (+)
Object distance u is always negative
Convex: always virtual, erect, diminished
Parallel mirrors → infinite images
1
Laws of Reflection
The Two Laws
Coplanarity: Incident ray, reflected ray, and normal at point of incidence all lie in the same plane.
Equal Angles:∠i = ∠r — angle of incidence equals angle of reflection (both measured from normal).
These laws apply to both plane and spherical mirrors.
Regular Reflection
Smooth, polished surfaces (mirrors, calm water)
Parallel rays stay parallel after reflection
Forms a clear, sharp image
Diffuse Reflection
Rough, uneven surfaces (paper, walls)
Parallel rays scatter in all directions
We see objects from any angle because of this
2
Plane Mirror Image
Property
Detail
Nature
Virtual and Erect
Size
Same size as object (m = 1)
Distance
Image distance = Object distance (behind mirror)
Lateral Inversion
Left ↔ Right swapped. AMBULANCE written reversed so it reads correctly in a mirror.
3
Two Mirrors — Multiple Images
Formula: n = (360°/θ) − 1
Angle θ
360°/θ
n (images)
90°
4 (even)
3
60°
6 (even)
5
45°
8 (even)
7
0° (Parallel)
∞
∞
1
Types of Spherical Mirrors
Concave Mirror
Reflecting surface curves inward
Silvered surface on the inner (concave) face
Gray backing on the outer (convex) face
Called Converging mirror
F is in front — real focus; f is negative
Convex Mirror
Reflecting surface curves outward
Silvered surface on the outer (convex) face
Gray backing on the inner (concave) face
Called Diverging mirror
F is behind — virtual focus; f is positive
2
Key Terms
Term
Symbol
Definition
Pole
P
Geometric centre of the reflecting surface. All distances measured from P.
Centre of Curvature
C
Centre of the sphere of which the mirror is a part.
Radius of Curvature
R
Distance PC (= 2f). Negative for concave.
Principal Axis
—
Line through P and C, perpendicular to mirror at P.
Principal Focus
F
Concave: parallel rays converge here (real). Convex: parallel rays appear to diverge from here (virtual).
Focal Length
f
PF distance. f = R/2.
3
Concave Mirror — 6 Cases
Case
Object Position
Image Position
Nature
Size
1
At Infinity
At F
Real & Inverted
Point (highly diminished)
2
Beyond C
Between F & C
Real & Inverted
Diminished
3
At C
At C
Real & Inverted
Same size
4
Between C & F
Beyond C
Real & Inverted
Magnified
5
At F
At Infinity
Real & Inverted
Highly Magnified
6⭐
Between F & P
Behind the mirror
Virtual & Erect
Magnified
⭐ Case 6 is the most exam-important! Only case giving virtual, erect, magnified image from a concave mirror.
🔬
Plane Mirror Simulations
Sim 1 — Single Plane Mirror
Object Distance
Object Height
Incident ray
Reflected ray
Normal
Virtual extension / image
u = — |
v = — |
∠i = — = ∠r = — |
Image: Virtual, Erect, Same size
Sim 2 — Two Plane Mirrors
Mode: Parallel |
θ = 0° |
n = ∞
🔬
Spherical Mirror Simulator
Concave Mirror — drag object ←→ or use slider
Object Distance
Object Height
Ray 1: parallel→F
Ray 2: through F→parallel
Ray 3: through C (retraces)
Virtual extension (behind mirror)
u = — |
v = — |
f = — |
m = — |
Image: —
Jump to Case —
Move the slider or drag the object on the diagram to see different cases.
1
Mirror Formula
1/v + 1/u = 1/f
All distances from Pole P. Apply sign convention.
2
Magnification
m = −v/u
Linear magnification
m = hᵢ / h₀
Image height / Object height
m value
Meaning
|m|>1
Magnified
|m|=1
Same size
|m|<1
Diminished
m positive
Virtual & Erect
m negative
Real & Inverted
3
Cartesian Sign Convention
Quantity
Sign
Reason
u (object distance)
Always −ve
Object in front, against incident direction
v (real image)
−ve
In front of mirror
v (virtual image)
+ve
Behind mirror
f — Concave
−ve
F in front of mirror
f — Convex
+ve
F behind mirror
Heights above axis
+ve
Above principal axis
1
Uses of Concave Mirrors
Shaving / Makeup Mirror
Face placed between F and P → virtual, erect, magnified image (Case 6).
Dentist's Mirror
Tooth between F and P → magnified virtual image for easy examination.
Headlights / Searchlights
Bulb at F → reflected rays emerge as parallel beam (reverse of Case 5).
Solar Furnace
Concentrates parallel sunrays at F → very high temperature.
2
Uses of Convex Mirrors
Rear-View Mirror
Always erect, diminished + wider field of view → driver sees larger area behind.
Security Mirrors
Shop corners — wide field of view from one mirror.