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Refraction at a boundary

Key idea: Light changes speed at a boundary. At an angle, it bends towards the normal when it slows down and away when it speeds up; along the normal, its direction stays the same.

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A straw standing in a glass of water looks bent at the surface, even though it is straight. Light from the straw changes direction as it leaves the water, so your eye traces it back to the wrong place. This change of direction at a boundary is refraction, and the direction a ray bends depends on whether the light speeds up or slows down. Angles are measured from the normal, as for reflection.

Refraction at a boundary

Refraction occurs at a boundary where light passes between transparent materials with different light speeds. At oblique incidence, the ray changes direction; along the normal, its speed changes but its direction does not. In glass and water, light is slower than in air.

To see why a change of speed bends the ray, think of a wide beam of light reaching a glass block at an angle. One edge of the beam enters the glass first and slows down, while the other edge is still travelling faster in the air. The beam swings round, like a column of marchers turning when one end reaches mud first, and travels on at a new angle, closer to the normal.

The terms are the same as for reflection, with one new angle:

  • the normal is a line at 90° to the boundary at the point where the ray crosses it;
  • the angle of incidence, i, is between the incident ray and the normal;
  • the angle of refraction, r, is between the refracted ray and the normal.

For a ray that passes through the boundary, the bend depends on its change of speed. Compare angles from the normal at that boundary:

How a ray bends at a boundary
The ray…ExampleDirection
slows downair into glass or waterbends towards the normal: r is smaller than i
speeds upglass or water into airbends away from the normal: the angle in air is the larger one
travels along the normal (i = 0°)air into glass, straight ondoes not change direction, although its speed still changes
A ray passing through a parallel-sided glass blockA rectangular glass block lies horizontally with air above and below it. A ray in the air travels down to the right and meets the top face at an angle of incidence of 50 degrees to the dashed normal. Inside the glass it bends towards the normal: the angle of refraction is approximately 31 degrees. It crosses the block and meets the bottom face, where it meets that face's normal at approximately 31 degrees. It leaves into the air bending away from the normal, at 50 degrees. The emergent ray is parallel to the incident ray but shifted sideways; a dotted line continuing the incident ray shows the shift. The glass has sin i / sin r = 1.50; displayed refraction angles are rounded to the nearest degree. The ray slows on entry and speeds up on exit.airglass blockairnormali = 50°r = 31°31°50°incident rayemergent raybends towards the normalthen away from it
A ray passing through a parallel-sided glass blockA rectangular glass block lies horizontally with air above and below it. A ray in the air travels down to the right and meets the top face at an angle of incidence of 50 degrees to the dashed normal. Inside the glass it bends towards the normal: the angle of refraction is approximately 31 degrees. It crosses the block and meets the bottom face, where it meets that face's normal at approximately 31 degrees. It leaves into the air bending away from the normal, at 50 degrees. The emergent ray is parallel to the incident ray but shifted sideways; a dotted line continuing the incident ray shows the shift. The glass has sin i / sin r = 1.50; displayed refraction angles are rounded to the nearest degree. The ray slows on entry and speeds up on exit. airglass blockairnormalincident rayemergent raybends towards the normalthen away from iti = 50°r = 31°31°50°
Entering glass, the ray bends towards the normal (50° to 31°); leaving, it bends away. The emergent ray is parallel; angles are rounded.

Worked example 1

Describing a ray through a glass block

Problem

Use the figure. Describe what happens to the ray at each face of the block, using the terms normal, angle of incidence and angle of refraction.

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  1. Top face: air into glass

    Method

    The ray meets the top face with an angle of incidence of 50°.

    Reason

    It slows down as it enters the glass.

    Working

    Answer

    It bends towards the normal. The angle of refraction is about 31°, smaller than i.

  2. Bottom face: glass into air

    Method

    Inside the block, the ray meets the bottom face at about 31° to that face’s normal.

    Reason

    It speeds up as it leaves the glass.

    Working

    Answer

    It bends away from the normal and leaves at 50°.

  3. Compare the rays

    Working

    Answer

    The two faces are parallel, so the bends are equal and opposite. The emergent ray is parallel to the incident ray, shifted sideways.

Check your understanding 1 Predict from the change of medium

A ray meets the water–air boundary at a non-zero angle to the normal and passes into air, where light is faster. Which way does it bend?
A ray enters a glass block along the normal. What changes?
Show answer

For water into air at the stated non-zero angle, light speeds up and bends away from the normal. For entry into glass along the normal, its speed decreases but direction stays the same: both normal-based angles are 0°. A ray can change speed without changing direction.

Check your understanding 2 Why the ray bends

Define the angle of refraction. Light travels at 2.4 × 10⁸ m/s in material P and 2.0 × 10⁸ m/s in material Q. A ray passes obliquely from P into Q. Predict its bend. What would change if it crossed along the normal instead?

Show answer

The angle of refraction is the angle between the refracted ray and the normal. The speed decreases from P to Q, so the oblique ray bends towards the normal and its angle of refraction is smaller than its angle of incidence. Along the normal, the speed would still decrease but the ray would not change direction: both angles would be 0°.

The size of each angle, and the refractive index that links it to the speed of light, are calculated in Refraction calculations.

Common mistakes

  • Measuring i or r from the boundary instead of from the normal.
  • Saying light always bends towards the normal. It bends towards the normal only when it slows down, and away from it when it speeds up.
  • Saying a ray along the normal does not refract at all. It does not change direction, but its speed still changes.

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