(i) refraction of light; refractive index; n = c/v; n sin i = constant at…

The idea

Refraction is the change in direction of light when it crosses a boundary between media, caused by a change in speed. The refractive index n of a medium is defined by n = c/v, where c is the speed of light in a vacuum (3.00 × 10⁸ m s⁻¹) and v is the speed in the medium; n is dimensionless and always ≥ 1. At a boundary, n sin i is constant, where i is measured from the normal, not the surface. For light going from medium 1 to medium 2, n₁ sin i₁ = n₂ sin i₂. Example: light entering glass (n = 1.50) from air at i = 30.0° gives sin r = sin 30.0°/1.50 = 0.333, so r = 19.5°. A larger n means greater bending towards the normal on entry.

What earns the marks

• Refraction is the change in direction of a wave at a boundary due to a change in speed in the new medium.
• Refractive index is defined as n = c/v, the ratio of the speed of light in a vacuum to its speed in the medium.
• n is dimensionless and has a value greater than or equal to 1 for a material medium.
• The general boundary relationship is n₁ sin i₁ = n₂ sin i₂, with angles measured from the normal.
• For light entering a denser medium (larger n), the ray bends towards the normal; leaving it, the ray bends away.
• A typical calculation: sin r = sin i/n, e.g. sin r = sin 30.0°/1.50 = 0.333 giving r = 19.5°.

Common mistakes and how to put them right

• Measuring the angle from the boundary surface instead of the normal.

  Put it right: I and r are always angles between the ray and the normal.

• Writing n = v/c rather than n = c/v.

  Put it right: n compares the vacuum speed to the medium speed, so n ≥ 1.

• Assuming n sin i is constant for all boundaries regardless of the second medium.

  Put it right: n₁ sin i₁ = n₂ sin i₂ links the two specific media.

• Treating n as having units.

  Put it right: n is a dimensionless ratio of two speeds.

Exam tips

• Sketch the normal as a dashed line at 90° to the surface before marking any angle.
• Check that your calculated r is smaller than i when light enters a higher-n medium.
• Keep speeds in m s⁻¹ and use c = 3.00 × 10⁸ m s⁻¹ consistently in n = c/v.