Also, this physics grades 9-10 lesson on refractive index notes gives the key ideas first, then worked examples and diagrams. After that, practise with the worksheet on refractive index and check yourself with the quiz.
Quick answer: Refraction is the bending of light as it changes speed between materials. The refractive index n = sin i ÷ sin r gives its size. In addition, beyond the critical angle, a dense material totally reflects the light inside it. Moreover, converging lenses focus parallel rays to a principal focus and form real or virtual images.
Level: Physics grades 9-10 (GCSE · IGCSE · O Level · Class 9-10) · Curriculum: IGCSE 3.2
Refractive index notes: the key ideas
How does light reflect from a mirror?
When a ray of light hits a smooth surface, it bounces off in a predictable direction. Moreover, to describe it, we draw the normal, a line at 90° to the surface at the point where the ray lands.
Law of reflection: the angle of incidence equals the angle of reflection (i = r). Also, the incident ray, the reflected ray and the normal all lie in the same plane.
What is refraction and how do you calculate refractive index?
Furthermore, light travels fastest in a vacuum, at 3.0 × 10⁸ m/s. In a denser material such as glass it slows down, and when a ray meets the boundary at an angle, the change of speed makes it change direction. In addition, we call this bending refraction.
Refraction is the change of direction of a wave when it passes from one material into another, caused by a change in its speed. Also, the refractive index n of a material tells you how strongly it bends light.
The refractive index formula
n = sin i ÷ sin r
n = refractive index (no unit), i = angle of incidence in air (°), r = angle of refraction in the material (°). Also n = c ÷ v, where c is the speed of light in air and v the speed in the material.
A ray entering a denser material bends towards the normal. However, a ray leaving it bends away from the normal. Finally, a ray travelling along the normal (0°) is not bent at all.
Chiamaka in Lagos shines a ray onto an acrylic block at i = 40°. She measures r = 25°. In addition, calculate the refractive index.
n = sin 40° ÷ sin 25° = 0.643 ÷ 0.423 = 1.52
Refractive index of common materials
| Material | Refractive index n | Speed of light (10⁸ m/s) |
|---|---|---|
| Air | 1.00 | 3.00 |
| Water | 1.33 | 2.26 |
| Perspex | 1.49 | 2.01 |
| Glass | 1.52 | 1.97 |
| Diamond | 2.42 | 1.24 |
A higher n means slower light and stronger bending. Diamond bends light far more than water does.
What is total internal reflection?
When light tries to leave a dense material for air, it bends away from the normal. Moreover, make the angle of incidence larger and the refracted ray swings closer and closer to the surface. Furthermore, at one special angle it just skims along it.
Furthermore, the critical angle c is the angle of incidence inside a dense material for which the refracted ray travels along the boundary (r = 90°). Moreover, for any larger angle, total internal reflection occurs: all the light reflects back into the material.
The critical angle formula
sin c = 1 ÷ n
c = critical angle (°), n = refractive index of the material (boundary with air).
Total internal reflection needs two conditions: the light travels from a denser to a less dense material, and the angle of incidence is greater than c.
Also, calculate the critical angle for water, n = 1.33.
sin c = 1 ÷ 1.33 = 0.752, so c = 48.8°. Water totally reflects a ray that hits the surface at 55° from inside.
Measuring angles from the surface instead of from the normal. You measure every angle in reflection, refraction and critical-angle work from the normal.
In addition, optical fibres carry internet signals as light that bounces by total internal reflection along a thin glass strand. Moreover, prisms in binoculars and bicycle reflectors work the same way.
How do converging lenses form images?
A converging (convex) lens is thicker in the middle and refracts parallel rays so that they meet at the principal focus F. Also, the distance from the lens to F is the focal length f. Furthermore, to find an image you only need two of three special rays:
- A ray parallel to the principal axis refracts through the principal focus on the far side.
- Then, a ray through the centre of the lens carries straight on.
- Finally, a ray through the near principal focus emerges parallel to the axis.
Magnification of a lens
magnification m = image height ÷ object height
m has no unit. If m is greater than 1 the image is bigger than the object.
Mei in Singapore photographs a leaf 4.0 cm long. In addition, its image on the sensor is 1.2 cm long. Also, calculate the magnification.
m = 1.2 ÷ 4.0 = 0.30. Furthermore, the image is smaller than the object.
Real and virtual images
| Object position | Image | Used in |
|---|---|---|
| Beyond 2F | Real, inverted, smaller | Camera |
| Between F and 2F | Real, inverted, larger | Projector |
| Closer than F | Virtual, upright, larger | Magnifying glass |
A real image can be caught on a screen. A virtual image cannot: the rays only appear to come from it, as when you look through a magnifying glass.
In addition, draw the two easy rays first, one parallel to the axis and one through the centre, with a ruler. Where they cross is the top of the image. Moreover, always add arrows to every ray.
- Law of reflection: angle of incidence i = angle of reflection r, both from the normal.
- Furthermore, refractive index: n = sin i ÷ sin r = c ÷ v.
- critical angle: sin c = 1 ÷ n; total internal reflection needs i greater than c.
- A converging lens focuses a parallel beam at the principal focus F.
- magnification m = image height ÷ object height.
Bending light: refraction, critical angle and lenses: frequently asked questions
What is the formula for refractive index?
n = sin i ÷ sin r, where i is the angle in air and r is the angle in the material, both measured from the normal. You can also write n = c ÷ v, the speed of light in air divided by its speed in the material.
When does total internal reflection happen?
It happens when light travels from a denser material towards a less dense one and the angle of incidence is bigger than the critical angle. The material then reflects all the light back, with none refracted out.
How do you find the critical angle?
use sin c = 1 ÷ n for a boundary with air. For glass with n = 1.50, sin c = 0.667, so c = 41.8°.
What is the difference between a real and a virtual image?
A real image forms where light rays actually meet, and you can show it on a screen. A virtual image forms where rays only appear to come from, so you cannot catch it on a screen.
Why does a ray bend towards the normal in glass?
In addition, light travels more slowly in glass than in air. The side of the wavefront that enters first slows first, which turns the ray towards the normal.
