Physics · Lesson 16

Optics — Mirrors, Lenses & Light

Reflection Refraction Snell's Law Lens Equation

Light travels in straight lines until it hits something. A mirror reflects it by equal angles; a lens refracts it by Snell's law. These two principles — reflection and refraction — underlie cameras, telescopes, glasses, microscopes, fiber optics, and the human eye.

Who Was Ibn al-Haytham?

Ibn al-Haytham (965–1040) was an Arab mathematician and physicist who wrote Book of Optics (Kitab al-Manazir), establishing the first rigorous theory of vision, reflection, and refraction. He used controlled experiments and geometry to prove that light enters the eye from external objects — overturning Greek theories that the eye emits rays. Often called the "father of optics," his work influenced European science for centuries.

Core Concepts

Law of Reflection

When light hits a mirror, the angle of incidence equals the angle of reflection — both measured from the normal (perpendicular) to the surface.

θᵢ = θᵣ

θᵢ = angle of incidence (from normal)

θᵣ = angle of reflection (from normal)

Snell's Law (Refraction)

When light crosses from one medium to another it bends. The amount of bending depends on the refractive indices of both media.

n₁ · sin θ₁ = n₂ · sin θ₂

n = refractive index (n = c/v)

θ₁ = angle in medium 1

θ₂ = angle in medium 2

Thin Lens Equation

1/f = 1/dₒ + 1/dᵢ

f = focal length (m)

dₒ = object distance (m)

dᵢ = image distance (m)

Convex lens converges light to a focal point. Concave lens diverges light. Total internal reflection occurs when θ exceeds the critical angle — the principle behind fiber optics.

Interactive Simulator

Use the panel controls to switch mode and adjust the angle of incidence. The yellow ray is incident; orange is reflected or refracted.

ModeMirror

Angle In40°

Angle Out40°

Real-World Applications

👓

Eyeglasses & Contact Lenses Corrective lenses refract light to compensate for the eye's own focal length being too long or too short.

🔭

Telescopes & Microscopes Series of lenses or mirrors gather and magnify light, allowing us to see distant stars or microscopic cells.

💡

Fiber Optic Cables Total internal reflection traps light inside glass fibers, carrying internet data at nearly the speed of light.

📷

Camera Lenses Compound lens systems focus and correct light onto digital sensors, controlling depth of field and zoom.

Explore Advanced Scenarios

This interactive Ray Optics simulator demonstrates refraction, reflection, dispersion, and more. Explore 60+ optical phenomena in real-time:

The chromatic dispersion scenario above shows how different wavelengths refract at slightly different angles — the principle behind prisms and rainbows. Use the simulator's toolbar to:

Switch to other optical systems (lenses, mirrors, fibers, etc.)
Adjust ray properties and surface angles
Measure angles and distances
Explore the complete Ray Optics Gallery with 60+ preset scenarios

Practice Problems

Apply the law of reflection, Snell's law, and the lens equation.

Easy1. A light ray hits a flat mirror at 30° from the normal. At what angle (in degrees) does it reflect?

Hint: Law of reflection — angle of incidence = angle of reflection.

Easy2. Which type of lens converges parallel rays to a focal point?

Hint: Convex = thicker in the middle = converging.

Medium3. Light travels from glass (n₁=1.5) into air (n₂=1.0) at θ₁=30°. Use Snell's law to find θ₂ in degrees (1 decimal).

Hint: sin θ₂ = 1.5×sin(30°)/1.0 = 0.75. θ₂ = arcsin(0.75) ≈ 48.6°

Medium4. A convex lens has f=10 cm. An object is dₒ=30 cm away. Find the image distance dᵢ in cm.

Hint: 1/10 = 1/30 + 1/dᵢ → 1/dᵢ = 1/10 − 1/30 = 2/30 → dᵢ = 15 cm

Challenge5. Find the critical angle θc for total internal reflection in glass (n=1.5) going into air (n=1.0). Give your answer in degrees (1 decimal). [sin θc = 1/1.5]

Hint: sin θc = n_air/n_glass = 1/1.5 ≈ 0.667. θc = arcsin(0.667) ≈ 41.8°