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# Success in Maths and Science unlocks opportunities

## 5.8 Summary (ESBNC)

Presentation: 23TP

• Light rays are lines which are perpendicular to the light’s wavefronts. In geometrical optics we represent light rays with arrows with straight lines.

• Light rays reflect off surfaces. The incident ray shines in on the surface and the reflected ray is the one that bounces off the surface. The normal is the line perpendicular to the surface where the light strikes the surface.

• The angle of incidence is the angle between the incident ray and the surface, and the incident ray, reflected ray, and the normal, all lie in the same plane.

• The Law of Reflection states the angle of incidence ($$\theta_{i}$$) is equal to the angle of reflection ($$\theta_{r}$$) and that the reflected ray lies in the plane of incidence.

• Light can be absorbed and transmitted.

• The speed of light, $$c$$, is constant in a given medium and has a maximum speed in vacuum of $$\text{3} \times \text{10}^{\text{8}}$$ $$\text{m·s^{-1}}$$

• Refraction occurs at the boundary of two media when light travels from one medium into the other and its speed changes but its frequency remains the same. If the light ray hits the boundary at an angle which is not perpendicular to or parallel to the surface, then it will change direction and appear to `bend'.

• The refractive index (symbol $$n$$) of a material is the ratio of the speed of light in a vacuum to its speed in the material and gives an indication of how difficult it is for light to get through the material.

$$n = \frac{c}{v}$$

• Optical density is a measure of the refracting power of a medium.

• The normal to a surface is the line which is perpendicular to the plane of the surface.

• The angle of incidence is the angle defined between the normal to a surface and the incoming (incident) light ray.

• The angle of refraction is the angle defined between the normal to a surface and the refracted light ray.

• Snell's Law gives the relationship between the refractive indices, angles of incidence and reflection of two media.

$$n_1 \sin \theta_1 = n_2 \sin \theta_2$$

• Light travelling from one medium to another of lighter optical density will be refracted towards the normal.

Light travelling from one medium to another of lower optical density will be refracted away from the normal.

• The critical angle of a medium is the angle of incidence when the angle of refraction is $$\text{90}$$$$\text{°}$$ and the refracted ray runs along the interface between the two media.

• Total internal reflection takes place when light travels from one medium to another of lower optical density. If the angle of incidence is greater than the critical angle for the medium, the light will be reflected back into the medium. No refraction takes place.

• Total internal reflection is used in optical fibres in telecommunication and in medicine in endoscopes. Optical fibres transmit information much more quickly and accurately than traditional methods.