Reflection and Refraction of Light

Understand how light bounces off mirrors and bends when it passes between different materials.

Light Travels in Straight Lines

Light travels in straight lines called rays. We use ray diagrams to trace its path.

Reflection

When light hits a smooth surface it reflects (bounces off).

Law of Reflection

\theta_i = \theta_r

Both angles are measured from the normal (line perpendicular to the surface).

Specular reflection — smooth surface (mirror): clear image.
Diffuse reflection — rough surface (paper): scattered light, no clear image.

Refraction

When light passes from one transparent material into another, it changes speed and bends.

Light bends toward the normal when entering a denser medium.

Snell's Law

n_1 \sin\theta_1 = n_2 \sin\theta_2

n = refractive index of the medium. Higher n means slower, denser medium.

Medium	Refractive index n
Vacuum	1.00
Air	≈ 1.00
Water	1.33
Glass	≈ 1.5
Diamond	2.42

Note Light bends toward the normal when entering a denser medium (higher n) and away from the normal when exiting to a less dense medium.

Total Internal Reflection

If light hits the boundary at an angle greater than the critical angle, it reflects completely back into the denser medium. Optical fibres use this principle.

1
Draw the normal
A dashed line perpendicular to the surface at the point of incidence.
2
Measure angles from the normal
Not from the surface itself.
3
Apply the correct law
Reflection: θ_i = θ_r. Refraction: Snell's law.

A ray in air hits water at an incidence angle of 30°. Find the refraction angle. (n_water = 1.33)

$1.00 \times \sin 30° = 1.33 \times \sin\theta_2 \implies \sin\theta_2 = \frac{0.5}{1.33} \approx 0.376 \implies \theta_2 \approx 22°$

Real world: corrective lenses (glasses)

A short-sighted person's eye refracts light too strongly, focusing the image in front of the retina. Concave (diverging) lenses are prescribed to bend light rays outward before they enter the eye, allowing them to focus correctly on the retina. Snell's law governs how lens curvature and refractive index are calculated for each prescription.

Real world: optical fibre internet cables

Optical fibres carry internet data as pulses of light. When light travels along the fibre and hits the glass-air boundary at an angle greater than the critical angle, total internal reflection keeps the light trapped inside the fibre. A single fibre hair-thin can carry billions of bits per second around the world.

Real world: swimming pool depth illusion

A swimming pool looks shallower than it actually is because light from the bottom refracts away from the normal when it enters the air (going from dense water to less-dense air). Your eye traces the ray back in a straight line and perceives a shallower apparent depth — a direct consequence of Snell's Law.

Tip Always measure angles of incidence and reflection from the normal (perpendicular to the surface), not from the surface itself. This is the most common error in ray diagram questions.

Practice Problems

A ray hits a mirror at 40° from the normal. What is the angle of reflection?

Show answer

θ_r = 40°.

Does light bend toward or away from the normal when going from water to air?

Show answer

Away from the normal (it speeds up).

Name one everyday application of total internal reflection.

Show answer

Optical fibre cables (or diamond sparkle, periscopes, etc.).