Reflection and Refraction of Light: Laws, Snell's Law, and Examples

Every time you look in a mirror, see a rainbow, or watch a straw appear bent in a glass of water, you are witnessing two of the most fundamental behaviours of light: reflection and refraction. These phenomena arise because light is an electromagnetic wave that travels at different speeds in different media, and its path bends at every boundary between media. Understanding reflection and refraction is the foundation of all optics — from spectacles and cameras to optical fibres and laser surgery.

The Law of Reflection

The angle of incidence (θ_i) equals the angle of reflection (θ_r). Both angles are measured from the normal — the line perpendicular to the surface at the point of incidence. The incident ray, reflected ray, and normal all lie in the same plane.

This law holds for all types of reflection — flat (plane) mirrors, curved mirrors, and even rough surfaces (where the normal varies across the surface, causing diffuse reflection rather than specular reflection).

Refraction and the Refractive Index

When light passes from one medium to another, its speed changes. The refractive index n of a medium is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v):

Since light always travels slower in matter than in vacuum, n ≥ 1 for all real materials. Air: n ≈ 1.0003 (effectively 1.0). Water: n = 1.33. Glass: n ≈ 1.5. Diamond: n = 2.42.

Snell's Law

Snell's Law (also called the law of refraction) gives the angle of refraction when light crosses a boundary:

where n₁ is the refractive index of the first medium, θ₁ is the angle of incidence, n₂ is the refractive index of the second medium, and θ₂ is the angle of refraction. Both angles are measured from the normal.

Key consequences:

• Light entering a denser medium (n₂ > n₁) bends toward the normal (θ₂ < θ₁).

• Light entering a less dense medium (n₂ < n₁) bends away from the normal (θ₂ > θ₁).

• Light at normal incidence (θ₁ = 0°) does not bend — it passes straight through.

Worked Example: Snell's Law

Light in air (n = 1.0) hits a glass surface (n = 1.5) at 40° to the normal. Find the refraction angle.

Light bends toward the normal (25.4° < 40°) on entering the denser glass. ✓

Total Internal Reflection

When light travels from a denser medium to a less dense medium (n₁ > n₂), the refracted angle θ₂ > θ₁. As θ₁ increases, at some point θ₂ reaches 90° — the refracted ray travels along the surface. This angle is the critical angle θ_c:

For glass (n = 1.5) to air (n = 1.0): sinθ_c = 1/1.5 = 0.667 → θ_c = 41.8°.

For angles greater than θ_c, total internal reflection occurs — all light is reflected back into the denser medium. No refraction takes place. This is the principle behind:

Optical fibres: light enters a glass fibre and is totally internally reflected along its entire length with almost no loss, enabling high-bandwidth telecommunications. The fibre core has higher n than the surrounding cladding, ensuring TIR at all incidence angles above the critical angle.

Diamond brilliance: diamond's very high n (2.42) gives a critical angle of only 24.4° — much smaller than glass. Most light entering a diamond exceeds the critical angle and undergoes TIR many times before exiting, producing the characteristic sparkle (fire and brilliance) that makes cut diamonds so visually striking.

Prisms in binoculars: use TIR to reflect light and fold the optical path without the energy loss of metallic mirrors.

Why Does Refraction Cause a Straw to Look Bent?

When you look at a straw in a glass of water, the part below the water surface appears displaced from the part above. Your eye traces the light rays reaching it backward in a straight line — but the rays have been bent at the water-air interface. The brain, assuming straight-line travel, places the underwater straw tip at the wrong apparent position. This is why objects seen through water appear shallower than they are: apparent depth = real depth / n.

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