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FIGURE 119 The complete electromagnetic spectrum (From Mulligan,3 p 291)
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5 Light As we have seen from Fig 119, visible light occupies that portion of the electromagnetic spectrum consisting of wavelengths from 04 m (that is, 10 6 m) to 07 m From a physical point of view, the ultraviolet region, 04 with wavelengths shorter than 04 m, blends continuously into the visible region, which in turn blends continuously into the infrared region, with wavelengths longer than 07 m (Note that the infra in infrared and the ultra in ultraviolet refer to frequency, not wavelength) The distinguishing feature of the visible portion of the spectrum is the human eye s sensitivity to wavelengths between 04 and 07 m, in contrast to its insensitivity to infrared and ultraviolet radiation The human eye sees each different wavelength of the visible region as a different color; violet corresponds to 04 m and red to 07 m, and there is a continuous change from violet to blue-green to orange to yellow to red between these two limits In free space, the speed of all electromagnetic waves is the same This is not true in a material substance such as glass, where different wavelengths have different speeds
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Re ection and Refraction Consider a ray of light In an isotropic medium, rays c / n, where n is the are straight lines, along which energy travels at speed v refractive index of the medium Because n 1, the speed is less than the speed in
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vacuum, c 3 108 m / s The refractive index is a function of the wavelength (in vacuum) of the light Let a ray in medium 1 be incident on the interface with medium 2, making angle 1 with the normal to the interface (Fig 1110) Then, in general, there will be a re ected ray in medium 1 and a refracted ray in medium 2 such that 1 The three rays and the normal all lie in a common plane, the plane of incidence 2 The angle of incidence equals the angle of re ection, that is, 1 r 3 The directions of the incident and refracted rays are related by Snell s law: n1 sin If n1 n2 and
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exceeds the critical angle sin
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then there will be no refracted ray a phenomenon called total re ection or, from the point of view of medium 1, total internal re ection A displacement of light rays, ie refraction of light, is again clearly demonstrated in Fig 1111, where the path of a ray of light passes through a parallel-sided glass block The incident ray AB that has an angle of incidence enters the glass block at B The direction of the ray changes to BC such that the angle is less than angle , called the angle of refraction When the ray emerges from the glass at being greater than The nal emerging C, the direction changes to CD, angle ray CD is parallel to the incident ray AB In general, when entering a more dense medium from a less dense medium, light is refracted towards the normal and when it passes from a dense to a less dense medium it is refracted away from the normal Geometrical Optics Geometrical optics is concerned with the effects on light rays of mirrors (plane, concave, convex) and lenses (converging, diverging) Lenses are pieces of glass or other transparent material with a spherical surface on one or both sides When light is passed through a lens it is refracted
FIGURE 1110 Illustration of the light refraction (From Wells and Slusher,2 p 301)
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FIGURE 1111 Displacement of light rays
Lenses are used in spectacles, magnifying glasses and microscopes, telescopes, cameras and projectors There are a number of different shaped lenses, and two of the most common are shown in Fig 1112 Figure 1112a shows a bi-convex lens, so called since both its surfaces curve outwards Figure 1112b shows a bi-concave lens, so called since both of its surfaces curve inwards The line passing through the center of curvature of the lens surface is called the principal axis Figure 1112c shows a number of parallel rays of light passing through a bi-convex lens They are seen to converge at a point F on the principal axis Figure 1112d shows parallel rays of light passing through a bi-concave lens They are seen to diverge such that they appear to come from a point F, which lies between the source of light and the lens, on the principal axis In both Figure cases, F is called the principal focus or the focal point, and the distance from F to the center of the lens is called the focal length of the lens It is assumed here that all lenses are thin (ie, their thickness is small compared to their radii of curvature) and that all rays are paraxial (ie, they make small angles with the axis of the optical system) The two basic relations for both mirrors and lenses are 1 do and do di where do di
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