2Everything Science www.everythingscience.co.zaIntroductionGeometrical optics is the study of how light interacts with materials and in particular with theshapes of the materials and the angles at which light rays hit it.Light rays are lines which are perpendicular to the light’s wavefronts. In geometrical opticswe represent light rays with arrows with straight lines.Light rays reflect off surfaces. Theincident ray shines in on the surface andthe reflected ray is the one that bouncesoff the surface. The normal is the lineperpendicular to the surface where thelight strikes the surface.The angle of incidence is the anglebetween the incident ray and the surface,and the incident ray, reflected ray, andthe normal, all lie in the same plane.
3Everything Science www.everythingscience.co.zaLaw of reflectionThe Law of reflection states the angle of incidence ( ) is equal to the angle ofreflection ( ) and that the reflected ray lies in the plane of incidence.θiθr
4Everything Science www.everythingscience.co.zaProperties of lightLight can be reflected, refracted, absorbed or transmitted. Reflection and refraction arecovered in more detail elsewhere in this chapter.Absorption of light is closely linked to reflection. Some wavelengths of light are reflected offobjects while others are absorbed by the object. This is what gives objects their colour.Light can be transmitted through objects. Objects that allow the transmission of light arecalled transparent and objects that do not are called opaque.The last property of light that we will look at is the speed of light. Light also has a maximumspeed at which it can propagate, and nothing can move faster than the speed of light.The speed of light, c, is constant in a given medium and has a maximum speed in vacuumis3×108m⋅s−1
5Everything Science www.everythingscience.co.zaRefractionRefraction occurs at the boundary of twomedia when light travels from one mediuminto the other and its speed changes but itsfrequency remains the same. If the light rayhits the boundary at an angle which is notperpendicular to or parallel to the surface,then it will change direction and appear to‘bend’.
6Everything Science www.everythingscience.co.zaRefractive index and optical densityThe refractive index (symbol n) of a material is the ratio of the speed of light in a vacuum toits speed in the material and gives an indication of how difficult it is for light to get throughthe material.If the refractive index, n, increases, the speed of light in the material, v, must decrease.Therefore light travels slower through materials of high refractive index, n.Optical density is a measure of the refracting power of a medium.n=cv
7Everything Science www.everythingscience.co.zaTerminology● 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 theincoming (incident) light ray.● The angle of refraction is the angle defined between the normal to a surface and therefracted light ray.
8Everything Science www.everythingscience.co.zaSnells lawSnell’s Law gives the relationship between the refractive indices, angles of incidence andreflection of two media.● Light travelling from one medium to another of lighter optical density will be refracted towardsthe normal.● Light travelling from one medium to another of lower optical density will be refracted awayfrom the normal.n1 sin θ1=n2 sinθ2
9Everything Science www.everythingscience.co.zaCritical angleThe critical angle is the angle of incidence where the angle of refraction is 90°. The light musttravel from an optically more dense medium to an optically less dense medium.θc=sin−1(n1n2)
10Everything Science www.everythingscience.co.zaTotal internal reflectionTotal internal reflection takes place when light travels from one medium to another of loweroptical 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 inendoscopes. Optical fibres transmit information much more quickly and accurately thantraditional methods.
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