Light – Reflection and Refraction · Lesson 10 of 15
The Refractive Index
“Light slows down in materials, proving even photons face traffic.”
• Define relative and absolute refractive index. • Relate refractive index to the speed of light. • Calculate speed or refractive index from given data. • Compare optical density using refractive-index values. • Distinguish optical density from mass density.
Two transparent materials may look equally clear yet bend light by different amounts. Refractive index provides a numerical way to compare them. Its physical basis is speed: light travels fastest in vacuum and more slowly in material media.
The ratio of the speed of light in the first medium to its speed in the second medium for light passing from medium one to medium two.
The ratio of the speed of light in vacuum, or approximately air, to the speed of light in the medium.
A refractive index of 1.50 means light travels 1.50 times as fast in vacuum as in that material. It does not mean that the material is 1.50 times heavier or that every ray bends by a fixed 1.50 degrees.
Optical Density
Of two media, the one with the larger refractive index and lower speed of light.
Optical density is not mass density. Kerosene can be optically denser than water because its refractive index is higher, even though its mass density is lower. When light goes from an optically rarer medium to a denser one, it slows and bends toward the normal; in the reverse direction it speeds up and bends away.
| Medium | Approximate refractive index |
|---|---|
| Air | 1.0003 |
| Ice | 1.31 |
| Water | 1.33 |
| Alcohol | 1.36 |
| Kerosene | 1.44 |
| Crown glass | 1.52 |
| Dense flint glass | 1.65 |
| Diamond | 2.42 |
Calculation Strategy
- Identify whether the problem asks for an absolute or relative index.
- Write the numerator speed for the medium from which light travels and the denominator speed for the medium it enters.
- Use n = c/v only when the reference medium is vacuum or air approximately.
- Keep speeds in the same units and remember that n is dimensionless.
- Check that the higher-index medium gives a lower calculated speed.
Problem
Light enters glass of refractive index 1.50. Find its speed in glass.
- 1.Given n = 1.50 and c = 3.0 × 10⁸ m s⁻¹.
- 2.From n = c/v, rearrange to v = c/n.
- 3.v = (3.0 × 10⁸)/1.50 = 2.0 × 10⁸ m s⁻¹.
- 4.The result is below c, as required for a material medium.
Problem
Light travels at 2.25 × 10⁸ m s⁻¹ in water and 2.00 × 10⁸ m s⁻¹ in glass. Find the refractive index of glass with respect to water.
- 1.Light travels from water, medium 1, into glass, medium 2.
- 2.Use n₂₁ = v₁/v₂ = vwater/vglass.
- 3.n(glass with respect to water) = 2.25/2.00 = 1.125.
- 4.The value above one agrees that glass is optically denser than water.
Problem
A material has n = 2.42. Find light speed in it and interpret the value.
- 1.Use v = c/n.
- 2.v = (3.0 × 10⁸)/2.42 ≈ 1.24 × 10⁸ m s⁻¹.
- 3.Light travels about 1.24 × 10⁸ m s⁻¹ in the material.
- 4.Vacuum speed is 2.42 times this speed; the large index indicates high optical density.
Refractive index has no unit because it is a ratio of speeds. A larger index means lower light speed, not greater mass density.
Quiz
Which medium is optically denser?
What is the unit of refractive index?
If n increases, what happens to light speed?
Which relation gives absolute refractive index?
Why can kerosene be optically denser than water but less massive per volume?
Practice Problems
- Find v for n = 1.25. Solution: v = c/n = 3.0 × 10⁸/1.25 = 2.4 × 10⁸ m s⁻¹.
- Find n when v = 1.5 × 10⁸ m s⁻¹. Solution: n = c/v = 3.0 × 10⁸/1.5 × 10⁸ = 2.0.
- Arrange water (1.33), glass (1.52) and diamond (2.42) by decreasing speed. Solution: Lower n means higher speed, so water, glass, diamond.
- If nAB = 1.20, find nBA. Solution: nBA = 1/nAB = 1/1.20 ≈ 0.833.
- Light moves at 2.0 × 10⁸ m s⁻¹ in A and 1.5 × 10⁸ m s⁻¹ in B. Find nBA and bending direction from A to B. Solution: nBA = vA/vB = 2.0/1.5 = 1.33. B is optically denser, so the ray bends toward the normal.
Key Takeaways
• Refractive index compares light speeds in different media. • Absolute refractive index is n = c/v and has no unit. • Relative index depends on the stated direction of travel. • Reversing two media gives a reciprocal relative index. • Larger refractive index means lower light speed and greater optical density. • Optical density and mass density are different properties.