Cheat Sheet — Light: Reflection & Refraction

🔦 Nature of Light

Light is a form of electromagnetic radiation visible to the human eye.
Travels in straight lines (rectilinear propagation).
Speed in vacuum: c = 3 × 10⁸ m/s
Luminous objects emit light (Sun, bulb). Non-luminous reflect light (Moon, book).
Transparent → transmits light; Translucent → partial; Opaque → blocks.

🪞 Laws of Reflection

Law 1: Angle of incidence = Angle of reflection ∠i = ∠r
Law 2: Incident ray, reflected ray, and normal all lie in the same plane.
These laws hold for ALL types of surfaces (smooth or rough).

Regular vs Diffuse Reflection

Regular: Smooth surface → parallel rays stay parallel (mirror).
Diffuse: Rough surface → rays scatter (wall, paper). Laws still obeyed at each point!

📷 Plane Mirror Image

Image is virtual, erect, same size.
Laterally inverted (left ↔ right swapped).
Image distance = Object distance from mirror.
If you walk towards a mirror at speed v, your image approaches you at speed 2v.

🔭 Spherical Mirrors — Basics

Term	Symbol	Meaning
Pole	P	Centre of mirror surface
Centre of Curvature	C	Centre of the sphere
Principal Focus	F	Midpoint of P and C
Radius of Curvature	R	Distance P → C
Focal Length	f	Distance P → F

R = 2f ⟹ f = R / 2

Concave Mirror — Image Table

Object at	Image at	Nature	Size
∞	F	Real, inv.	Point
Beyond C	Between F & C	Real, inv.	Diminished
At C	At C	Real, inv.	Same
Between C & F	Beyond C	Real, inv.	Enlarged
At F	∞	Real, inv.	Very large
Between F & P	Behind mirror	Virtual, erect	Enlarged

Convex mirror: Always virtual, erect, diminished — behind the mirror.

Mirror Formula & Magnification

1/v + 1/u = 1/f

u = object distance, v = image distance, f = focal length. All measured from pole P.

m = h'/h = −v/u

m > 0 → erect (virtual). m < 0 → inverted (real).
|m| > 1 → enlarged. |m| < 1 → diminished.

Uses of Mirrors

Concave Mirror	Convex Mirror
Torches, headlights, solar furnaces	Rear-view mirrors in vehicles
Shaving / make-up mirrors	Security mirrors in shops
Dentist's mirror	Wider field of view

🌊 Refraction of Light

Bending of light when it passes from one medium to another.
Caused by change in speed of light.
Rarer → Denser: Bends towards normal (speed decreases).
Denser → Rarer: Bends away from normal (speed increases).

Laws of Refraction (Snell's Law)

n₁ sin i = n₂ sin r

The ratio sin i / sin r = constant = ^n₂/_n₁ = ₁n₂ (refractive index of medium 2 w.r.t. 1).

Refractive Index

n = c / v

c = speed in vacuum, v = speed in medium.

Material	n
Air	1.0003 ≈ 1
Water	1.33
Glass	1.50 – 1.52
Diamond	2.42

Apparent Depth: Apparent Depth = Real Depth / n. This is why a pool looks shallower!

🔍 Spherical Lenses

Convex (converging): Thicker at centre, converges rays.
Concave (diverging): Thinner at centre, diverges rays.
Key points: O (optical centre), F₁, F₂, 2F₁, 2F₂.

Convex Lens Image Table

Object	Image	Nature	Size
∞	F₂	Real	Point
Beyond 2F₁	F₂ – 2F₂	Real	Diminished
At 2F₁	At 2F₂	Real	Same
F₁ – 2F₁	Beyond 2F₂	Real	Enlarged
At F₁	∞	Real	Very large
O – F₁	Same side	Virtual	Enlarged

Concave lens: Always virtual, erect, diminished — between F₁ and O.

Lens Formula & Power

1/v − 1/u = 1/f

Magnification: m = h'/h = v/u

Power of a Lens

P = 1/f (f in metres → P in Dioptres)

Convex → P is positive
Concave → P is negative
Combination: P = P₁ + P₂ + ...

📐 Sign Convention (New Cartesian)

All distances measured from pole (mirror) or optical centre (lens).
Distances in the direction of incident light = +ve.
Distances against incident light = −ve.
Heights above principal axis = +ve; below = −ve.

	Concave M	Convex M	Convex L	Concave L
u	−	−	−	−
f	−	+	+	−
v (real)	−	—	+	—
v (virtual)	+	+	−	−

📏 Ray Diagram Rules

Mirrors (use any 2)

Parallel to axis → passes through / appears from F.
Through F → reflects parallel to axis.
Through C → retraces path.
At pole → reflects with ∠i = ∠r.

Lenses (use any 2)

Parallel to axis → passes through / appears from F₂ (convex) or F₁ (concave).
Through optical centre O → undeviated.
Through F₁ → emerges parallel to axis.

🧠 Memory Tricks

"CAVE" for Concave: C = Converging, A = All images (real+virtual), V = Various sizes, E = Everyday uses (torch, shaving).
"VED" for Convex mirror: V = Virtual, E = Erect, D = Diminished (always).
Mirror formula: "VUF" → 1/V + 1/U = 1/F.
Lens formula: "V minus U equals F" → 1/v − 1/u = 1/f (lens has a MINUS).
Sign trick: Object is ALWAYS on the left → u is ALWAYS negative.
"n = c/v" — "Never Compromise on Values" (n = c over v).

⚠️ Common Board Mistakes

❌ Forgetting sign convention — u should be −ve always.
❌ Confusing mirror and lens formulas: mirror has +, lens has −.
❌ Writing R = f (correct: R = 2f).
❌ Not converting focal length to metres before calculating Power.
❌ Saying "convex mirror forms real images" — it NEVER does (always virtual).
❌ Drawing ray diagrams without labelling P, F, C / O, F₁, F₂.
❌ Mixing up ∠i measured from ray (wrong) vs from normal (correct).

🎯 Frequently Asked Numericals — Worked Examples

Mirror Problem

An object is placed 30 cm from a concave mirror of focal length 15 cm. Find image position and nature.

Solution: u = −30, f = −15

1/v = 1/f − 1/u = 1/(−15) − 1/(−30) = −1/30

v = −30 cm (real, inverted, same size — object at C, image at C).

m = −(−30)/(−30) = −1 → inverted, same size ✓

Lens Problem

A convex lens of focal length 20 cm has an object at 30 cm. Find v and m.

Solution: u = −30, f = +20

1/v = 1/f + 1/u = 1/20 + 1/(−30) = 1/60

v = +60 cm (real, inverted, on the other side).

m = v/u = 60/(−30) = −2 → inverted, 2× enlarged ✓