Refraction & Total Internal Reflection

Refractive index, Snell's law, critical angle, total internal reflection and optical fibres.

Spec Points Covered
  • Define the refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a medium. Determines how much light bends on entering the medium. of a material and calculate it from $n = c / c_{s}$.
  • Apply Snell's law: n1 sin $theta1 = n2 \sin$ theta2.
  • Calculate the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs. using sin $theta_{c} = n2 / n1$.
  • State the two conditions for total internal reflectionThe complete reflection of a wave at a boundary when the angle of incidence exceeds the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs. and the wave travels from a denser to a less dense medium..
  • Describe the structure of a step-index optical fibre and the role of cladding.
  • Explain material dispersion, modal dispersion, pulse broadening and absorption in optical fibres.
  • Describe methods to reduce signal degradation in optical fibres.
Notes
01 Refraction is a change in direction caused by a change in wave speed Refraction 3.3.2.3 → 02 Refractive index measures how much a medium slows down light Refractive index 3.3.2.3 → 03 Snell's law relates angles and refractive indices at a boundary $n_1 \sin \theta_1 = n_2 \sin \theta_2$ 3.3.2.3 → 04 The critical angle is where the refracted ray runs along the boundary Critical angle 3.3.2.3 → 05 Total internal reflection requires two conditions Total internal reflection (TIR) 3.3.2.3 → 06 Optical fibres use total internal reflection to transmit light signals 3.3.2.3 → 07 Material and modal dispersion cause pulse broadening Pulse broadening 3.3.2.3 → 08 Absorption and pulse broadening degrade signals -- but can be reduced 3.3.2.3 → 09 Worked example: calculating the angle of incidence at an optical fibre entry 3.3.2.3 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Refractive index
$$n = \frac{c}{c_s}$$
  • Where:
    • $n$ = refractive index (no units)
    • $c$ = speed of light in vacuum (\(3 \times 10^{8}\) m \(s^{-1}\))
    • $c_s$ = speed of light in the material (m \(s^{-1}\))
Always greater than 1. Air is treated as n = 1.
Critical angle
$$\sin \theta_c = \frac{n_2}{n_1}$$
  • Where:
    • $\theta_c$ = critical angle (degrees)
    • $n_1$ = refractive index of denser medium
    • $n_2$ = refractive index of less dense medium
Derived from Snell's law by setting theta_2 = 90 degrees. Only exists when n1 > n2.
Snell's law
$$n_1 \sin \theta_1 = n_2 \sin \theta_2$$
  • Where:
    • $n_1$ = refractive index of medium 1
    • $\theta_1$ = angle of incidence (degrees)
    • $n_2$ = refractive index of medium 2
    • $\theta_2$ = angle of refraction (degrees)
Angles measured from the normal. Material 1 is where the ray comes from.
Q Retrieval Practice All 12 Questions →
Q1. Define refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed..
The change in direction of a wave when it passes through a boundary between media of different optical densityMass per unit volume of a material. Measured in kg m⁻³., caused by a change in wave speedThe distance travelled by a wavefront per unit time..
Q2. State the equation for the refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a medium. Determines how much light bends on entering the medium. of a material.
n = c / c_s, where c is the speed of light in a vacuum and c_s is the speed of light in the material.
Q3. What happens to frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). when a wave refracts?
  • FrequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). stays the same.
  • Only speed and wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). change.
Q4. State Snell's law.
n1 sin theta1 = n2 sin theta2, where angles are measured from the normal.
Q5. Define the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refraction = 90 degrees). For angles greater than this, total internal reflection occurs..
The angle of incidence in the denser medium at which the angle of refraction is exactly 90 degrees.