Refraction and refractive index

Refraction

Refraction is the change in direction of a wave when it crosses a boundary and its speed changes. The frequency does not change, so the wavelength changes in proportion to the speed. A ray along the normal changes speed but not direction.

Refractive index

The refractive index of a material is n = c / v, where c = 3.00 x 10⁸ m/s is the speed of light in a vacuum and v is its speed in the material. n has no units and is at least 1 (air is about 1.00).

Snell's law

n1 sin θ1 = n2 sin θ2

Angles are measured from the normal. Going into a material with a higher refractive index, light slows down and bends towards the normal; going into a lower one, it speeds up and bends away.

Worked example

Light in air (n = 1.00) hits glass (n = 1.50) at 40° to the normal. Find the angle of refraction.

1. 1.00 x sin 40° = 1.50 x sin θ2
2. sin θ2 = 0.643 / 1.50 = 0.429

Answer: θ2 = 25.4°

Check yourself

1. Find the speed of light in glass of refractive index 1.50. Give your answer in units of 10⁸ m/s.
   Show answer

   2.00 x 10⁸ m/s. v = c / n = 3.00 x 10⁸ / 1.50 = 2.00 x 10⁸ m/s.

2. Light travels at 2.25 x 10⁸ m/s in water. Find the refractive index of water, to 3 s.f.
   Show answer

   1.33. n = c / v = 3.00 x 10⁸ / 2.25 x 10⁸ = 1.33.

3. Light passes from air into water (n = 1.33) at an angle of incidence of 50°. Find the angle of refraction in degrees, to 3 s.f.
   Show answer

   35.2 °. sin θ2 = sin 50° / 1.33 = 0.576, so θ2 = 35.2°.

4. Light passes from glass (n = 1.52) into water (n = 1.33) at 25° to the normal. Find the angle of refraction in degrees, to 3 s.f.
   Show answer

   28.9 °. sin θ2 = 1.52 x 0.423 / 1.33 = 0.483, so θ2 = 28.9°.

5. A ray in air hits a block at 60° to the normal and refracts at 35°. Find the refractive index of the block, to 3 s.f.
   Show answer

   1.51. n = sin 60° / sin 35° = 0.866 / 0.574 = 1.51.

6. When light passes from air into glass, which quantity stays the same?
   • Speed
   • Frequency
   • Wavelength
   • Direction (for oblique rays)
   Show answer

   Frequency. The frequency is set by the source; speed and wavelength both decrease.

7. Light passes at an angle into a material of higher refractive index. Which way does it bend?
   • Away from the normal
   • Along the boundary
   • It does not bend
   • Towards the normal
   Show answer

   Towards the normal. It slows down, so the angle from the normal becomes smaller.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)
• Pearson Edexcel IAL Physics Unit 2 (WPH12) question paper, January 2024: list of data (e, m_e, h, c, eV)

Last updated 7 November 2026. Spotted a mistake? Tell us.