Light and Electromagnetic Waves
Explore the electromagnetic spectrum, the laws of reflection and refraction, and learn to apply Snell's law to predict how light bends at boundaries between media.
The Electromagnetic Spectrum
Electromagnetic (EM) waves are transverse waves that can travel through a vacuum at the speed of light (c = 3.0 × 108 m/s). They consist of oscillating electric and magnetic fields perpendicular to each other and to the direction of travel. The EM spectrum arranges these waves by wavelength and frequency.
The Electromagnetic Spectrum
Radio
longest λ
Micro-wave
Infrared
Visible
Ultra-violet
X-rays
Gamma
shortest λ
← Increasing wavelength | Increasing frequency →
All EM waves travel at c = 3.0 × 108 m/s in a vacuum
Key equation: c = f × λ Since c is constant for EM waves in a vacuum, higher frequency means shorter wavelength, and vice versa.
Reflection and Refraction
When light hits a boundary between two media, it can be reflected (bounces back), refracted (bends as it passes through) or absorbed.
Law of Reflection
The angle of incidence (θi) equals the angle of reflection (θr). Both angles are measured from the normal (a line perpendicular to the surface).
θi = θr
Refraction
Light bends when it changes speed entering a new medium. Moving from a less dense to a more dense medium (e.g. air to glass), light bends towards the normal and slows down.
The refractive index (n) of a medium indicates how much it slows light: n = c / v.
Snell's Law: n1 sin(θ1) = n2 sin(θ2) where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction (measured from the normal).
Total Internal Reflection and Critical Angle
When light travels from a denser medium to a less dense medium (e.g. glass to air), it bends away from the normal. If the angle of incidence exceeds the critical angle, the light cannot escape and is completely reflected back inside the denser medium. This is called total internal reflection (TIR).
Finding the Critical Angle
At the critical angle, the refracted ray travels along the boundary (θ2 = 90°).
sin(θc) = n2 / n1
(where n1 > n2, i.e. light goes from denser to less dense medium)
Applications of Total Internal Reflection
Optical fibres: Light signals bounce repeatedly inside thin glass fibres, carrying data for telecommunications and medical endoscopes.
Diamonds: A high refractive index (n = 2.42) gives diamonds a small critical angle, so light reflects internally many times before emerging, creating sparkle.
Binoculars and periscopes: Prisms use TIR to redirect light paths without mirrors.
Key Vocabulary
Refractive Index (n)
A measure of how much a medium slows light. Defined as n = c / v, where c is the speed of light in a vacuum and v is the speed in the medium.
Normal
An imaginary line drawn perpendicular to a surface at the point where a ray hits. All angles in reflection and refraction are measured from the normal.
Critical Angle
The angle of incidence above which total internal reflection occurs. It only exists when light moves from a denser to a less dense medium.
Electromagnetic Spectrum
The complete range of EM waves ordered by wavelength/frequency: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays.
Worked Examples
Light enters glass (n = 1.50) from air (n = 1.00) at an angle of incidence of 30°. Find the angle of refraction.
Step 1: Apply Snell's law: n1 sin(θ1) = n2 sin(θ2).
Step 2: 1.00 × sin(30°) = 1.50 × sin(θ2). So 0.500 = 1.50 × sin(θ2).
Step 3: sin(θ2) = 0.500 / 1.50 = 0.333.
Answer: θ2 = sin-1(0.333) = 19.5°. The light bends towards the normal as expected.
Calculate the critical angle for glass (n = 1.50) to air (n = 1.00).
Step 1: sin(θc) = n2 / n1 = 1.00 / 1.50 = 0.667.
Answer: θc = sin-1(0.667) = 41.8°. Any angle of incidence above 41.8° will produce total internal reflection.
An EM wave has a frequency of 5.0 × 1014 Hz. What is its wavelength and what type of EM wave is it?
Step 1: λ = c / f = (3.0 × 108) / (5.0 × 1014).
Step 2: λ = 6.0 × 10-7 m = 600 nm.
Answer: Wavelength = 600 nm, which falls in the visible light range (orange-red light).
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
All electromagnetic waves travel at the same speed in:
Question 2
When light passes from air into glass, it bends:
Question 3
Total internal reflection can occur when light travels from:
Question 4
Which EM wave has the highest frequency?
Question 5
In the law of reflection, the angle of incidence is measured from:
Key Concepts Summary
- ●The EM spectrum ranges from radio waves (long λ) to gamma rays (short λ); all travel at c in a vacuum.
- ●Law of reflection: angle of incidence = angle of reflection (measured from the normal).
- ●Snell's Law: n1 sin(θ1) = n2 sin(θ2) predicts the angle of refraction.
- ●Total internal reflection occurs when light hits the boundary at an angle greater than the critical angle (denser to less dense medium).
- ●The refractive index n = c / v measures how much a medium slows light.