Refraction and refractive index

What you will learn

Refraction; n = c/v and n = sin i/sin r for air to medium.

Specification mapping: A2.1, A2.1.1

Prerequisites: A1.4

Physical principles

Refraction is a change in propagation direction caused by a change of wave speed across a boundary, except at normal incidence where speed changes without bending. Measure incidence i and refraction r from the normal, a line perpendicular to the boundary. For light entering a higher-index material from air, speed decreases and the ray bends towards the normal.

Absolute refractive index n = c/v is dimensionless; c is vacuum light speed and v is the phase speed in the material. For ordinary transparent materials in this course n exceeds one. At a stationary boundary frequency is unchanged, so the wavelength decreases with speed. Optical density refers to refractive index, not necessarily mass density.

For an air–material boundary, taking air index as one, n = sin i/sin r. More generally n₁ sin i = n₂ sin r. The air formula must not be applied blindly to two materials with non-unit incident index. Use degree mode for angles given in degrees. Dispersion means index can depend on wavelength.

Scientific diagram and interpretation

The ray enters higher-index glass from air and bends towards the normal. Angles are measured from the dashed normal. Geometry is schematic.

Equations and relationships

n = c/v = sin i/sin r (air incident approximation)

Worked examples and applications

Speed in glass

Take c = 3.00 × 10⁸ m s⁻¹ and n = 1.50. v = c/n = 2.00 × 10⁸ m s⁻¹. Wavelength falls to 1/1.50 of its vacuum value.

Angle of refraction

From air into n = 1.50 glass at i = 30.0°: sin r = sin 30.0°/1.50 = 0.3333; r = sin⁻¹(0.3333) = 19.5°. The smaller angle confirms bending towards the normal.

Common misconceptions

Angles measured from the surface give the wrong sine ratio. Frequency does not decrease on entry.

Examination technique

Draw and label the normal before calculating angles.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.