Animated Diagrams — Light: Reflection & Refraction

Laws of Reflection — Interactive

Drag the slider to change the angle of incidence and watch the reflected ray obey the law: ∠i = ∠r.

Angle of Incidence: 45°

Key Concept: The incident ray, reflected ray, and the normal at the point of incidence all lie in the same plane.

Regular vs Diffuse Reflection

Left: Regular reflection (smooth surface, e.g., mirror) — parallel rays remain parallel after reflection.
Right: Diffuse reflection (rough surface, e.g., wall) — parallel rays scatter in different directions. Both still obey the law of reflection at each point!

Board Tip: Diffuse reflection does NOT mean the laws of reflection are violated. The surface irregularities cause normals to point in different directions.

Concave & Convex Mirrors — Anatomy

Term	Symbol	Description
Pole	P	Centre of the mirror's reflecting surface
Centre of Curvature	C	Centre of the sphere of which the mirror is a part
Focus	F	Midpoint between P and C; where parallel rays converge (concave) or appear to diverge from (convex)
Radius of Curvature	R	Distance from P to C (R = 2f)
Principal Axis	—	Straight line through P and C

Image Formation — Concave Mirror

Object Position	Image Position	Nature	Size
At infinity	At F	Real, inverted	Highly diminished
Beyond C	Between F and C	Real, inverted	Diminished
At C	At C	Real, inverted	Same size
Between C and F	Beyond C	Real, inverted	Enlarged
At F	At infinity	Real, inverted	Highly enlarged
Between F and P	Behind mirror	Virtual, erect	Enlarged

Mnemonic: "Beyond C → diminished; At C → same; Between C and F → enlarged; At F → infinity; Between F and P → virtual magnified"

Snell's Law — Interactive Refraction

Light bends when passing from one medium to another. Drag the slider to change the angle and see how the refracted ray behaves.

∠ Incidence: 40° n₂: 1.50

n₁ sin(i) = n₂ sin(r) ⟹ sin(r) = n₁ sin(i) / n₂

Key Insight: When light goes from rarer to denser medium (n₂ > n₁), it bends towards the normal. When going denser to rarer, it bends away from the normal.

Refractive Index of Common Materials

Material	Refractive Index (n)	Speed of Light (km/s)
Vacuum / Air	1.00	3,00,000
Water	1.33	2,25,564
Glass (crown)	1.52	1,97,368
Diamond	2.42	1,23,967
Kerosene	1.44	2,08,333

Board Question: "Why does a swimming pool appear shallower?" — Because light bends away from normal when going from water (denser) to air (rarer). The apparent depth is less than real depth.
Apparent Depth = Real Depth / n

Convex & Concave Lenses

Image Formation — Convex Lens

Object Position	Image Position	Nature	Size
At infinity	At F₂	Real, inverted	Highly diminished (point)
Beyond 2F₁	Between F₂ and 2F₂	Real, inverted	Diminished
At 2F₁	At 2F₂	Real, inverted	Same size
Between F₁ and 2F₁	Beyond 2F₂	Real, inverted	Enlarged
At F₁	At infinity	Real, inverted	Infinitely large
Between F₁ and O	Same side as object	Virtual, erect	Enlarged

Concave Lens: Always forms a virtual, erect, diminished image between F and the optical centre — regardless of object position.

Power of a Lens

P = 1 / f (f in metres, P in Dioptres)

Convex lens → positive power (+D). Concave lens → negative power (−D).

For combination: P = P₁ + P₂ + P₃ + ...

Exam Example: A convex lens (f = +20 cm = +0.2 m) has P = +5 D. A concave lens (f = −50 cm = −0.5 m) has P = −2 D. Combined power = +5 + (−2) = +3 D → effective f = 1/3 m ≈ 33.3 cm.

Interactive Ray Diagram — Concave Mirror

Move the object along the principal axis to see how the image changes.

Object Distance |u|: 70

Interactive Ray Diagram — Convex Lens

Move the object to see real/virtual image formation through a convex lens.

Object Distance |u|: 60

Ray Diagram Rules

For Mirrors (use any 2)

A ray parallel to the principal axis passes through F (concave) or appears to come from F (convex) after reflection.
A ray passing through F reflects parallel to the principal axis.
A ray passing through C reflects back along the same path.
A ray hitting the pole reflects with ∠i = ∠r.

For Lenses (use any 2)

A ray parallel to the principal axis passes through F₂ (convex) or appears to diverge from F₁ (concave).
A ray through the optical centre O passes straight without deviation.
A ray through F₁ (convex) or directed at F₁ (concave) emerges parallel to the principal axis.

Mirror & Lens Formula Calculator

Mirror Formula

1/v + 1/u = 1/f

u (object dist, −ve): cm f (focal length): cm

Lens Formula

1/v − 1/u = 1/f

u (object dist, −ve): cm f (focal length): cm

Quick Reference — Sign Convention

Quantity	Concave Mirror	Convex Mirror	Convex Lens	Concave Lens
u	−ve	−ve	−ve	−ve
f	−ve	+ve	+ve	−ve
v (real image)	−ve	—	+ve	—
v (virtual image)	+ve	+ve	−ve	−ve