Optics

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13.1 Refraction of Light

  • Refraction is the change of direction that occurs when light passes non-normally across a boundary between 2 transparent substances with different refractive indecies.
  • Light rays bend towards the normal when they enter a more refractive substance, and away from the normal when they enter a less refractive substance.
  • No refraction takes place if a light ray is along the normal. 
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13.1 Refraction of Light (cont)

             (http://micro.magnet.fsu.edu/optics/lightandcolor/images/refractionfigure1.jpg)

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13.1 Refraction of Light (cont)

  • The angle of incidence is the angle between the incident light ray and the normal at the point of incidence. 
  • The angle of refraction is the angle between the refracted light ray and the normal at the point of incidence.
  • The angle of refraction at the incidence point is always less than the angle of incidence.
  • The ratio of sin i/ sin r of light rays in a substance is known as the refractive index, n. 
  • This is the same for all rays in a material- snell's law
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13.1 Refraction of Light (cont)

  • If I1 and R1 are the angles of incidence and refraction at the point of incidence, and I2 and R2 are the angles of incidence and refraction at the point of emergence, R1=I2 and I1=R2.
  • So Sin I2/ Sin R2 = 1/n
  • In a prism, the light rays refact towards the normal when it enters the prism, and then refracts the opposite way when it leaves. 
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13.2 More about Refraction

  • Refraction occurs because the speed of light waves is different in each substance.
  • The amount of refraction that takes place depends on the speed of the waves in each substance.
  • The refractive index of a substance =speed of light in a vacuum / speed of light in the substance.
  • so sin i/sin r = c in vacuum / c in substance.
  • In refraction  n1 x sin i=n2 x sin r.
  • The refractive index of air is 1.
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13.2 More about Refraction (cont)

  • We can use a glass prism to split a beam of white light into the colours of the spectrum by refraction.
  • White light is composed of light with a continuous range of wavelengths (red highest, violet lowest).
  • The shorter the wavelength, the greater the amount of refraction.
  • So each colour of the white light beam is refracted by a different amount.
  • The dispersive effect is because the waves all travel at different speeds (different wavelengths).
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13.2 More about Refraction (cont)

   (http://www.school-for-champions.com/science/images/light_dispersion1.gif)

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13.3 Total Internal Reflection

  • If the angle of incidence is increased to a value known as the critical angle, the light ray refracts along the boundary, perpendicular to the normal.
  • If the angle of incidence becomes greater than the critical angle, total internal reflection occurs at the boundary.
  • Total internal reflection can only take place if the incident substance (substance being entered) has a greater refractive index than the other substance.
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13.3 Total Internal Reflection (cont)

  • Sin (critical angle) = n2 / n1           n1>n2
  • Diamond has a very high refractive index, so it separates the colours of white light more than any other substance. 
  • A high refractive index gives diamond a low critical angle so total internal reflection can occurr more and more, so the colours spread out more when a light ray emerges.
  • This makes diamond sparkle with different colours. 
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13.3 Total Internal Reflection (cont)

  • Optical fibres transmit light (data) through a fibre using total internal reflection.
  • A core is completely surrounded by cladding.
  • As a light ray passes through the fibre, total internal reflection takes place at the core-cladding boundary.
  • The angle of incidence is always therefore greater than the critical angle of the core-cladding boundary. 
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13.3 Total Internal Reflection (cont)

  • Cladding stops two fibres coming into direct contact.
  • When this happens, light crosses from one fibre to the other. This crossover makes the signal insecure.
  • The core must be very narrow to prevent multipath dispersion.
  • In wider fibres, a light ray that passes directly through a fibre (no reflection) would take much less time than a ray that is indirectly reflected through.
  • This causes one pulse of light to merge with another.
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13.4 Double Slit Interference

  • To observe the interference of light, we can illuminate 2 closely spaced parallel splits using monochromatic light.
  • The light is first diffracted by a single slit, so that diffraction occurs and both double slits are correctly illuminated with monochromatic, coherent light.
  • The double slits act as sources of coherent light waves; they all have a constant phase difference. 
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13.4 Double Slit Interference (cont)

  • When the interference pattern is projected onto a screen, alternate bright and dark fringes are seen, known as Young's fringes.
  • This is the interference pattern from the overlapping of the diffracted light from each of the double slits.
  • When a bright fringe is formed, a light wave from one slit has reinforced another wave from the other slit. The two waves have arrived in phase.
  • When a dark fringe is formed, a light wave from one slit has cancelled out another wave from the other slit. The two waves have arrived 180' out of phase.
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13.4 Double Slit Interference (cont)

  • The distance between the centres of 2 bright (or 2 dark) fringes is called the fringe separation, w.
  • w = (wavelength x D) / s
  • D is the distance from slits to screen.
  • s is the slit spacing.
  • All are measured in metres. 
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13.4 Double Slit Interference (cont)

                           (http://kimheeley.edublogs.org/files/2012/11/double-slit-experiment-2b3ruiz.jpg)

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13.5 More about Interference

  • When white light is used in the double slit experiment, the fringe pattern contains a separation of colours.
  • The central fringe is white because every colour contributes at the centre of the pattern. 
  • The inner fringes are tinged with blue on the inner side and red on the outer side. This is because red light is spread out slightly more than blue light, so they do not overlap correctly.
  • The outer fringes are an indistinct background of the full white light colour spectrum. 
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13.6 Diffraction

  • Single slit diffraction can be demonstrated by directing a parallel beam of light at a slit, with the diffraction pattern forming on a white screen.
  • The pattern shows a central fringe that is twice as wide as the subsiquent fringes on either side.
  • The central fringe is far more intense than the other fringes, with intensity decreasing further from the central fringe. 
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13.6 Diffraction (cont)

  • The width of the fringes depends only on how much diffraction has taken place (more diffraction, wider fringes).
  • Making the slit narrower increases diffraction. 
  • Making the wavelength greater increases diffraction. 
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13.6 Diffraction (cont)

  • Young's double slit experiment can also be thought of as two single slit experiments.
  • If the slit separation is too small compared to the slit width, then the double slit diffraction becomes enveloped by the single slit pattern.
  • This means the intensity distribution of Young's fringes cannot exceed/disagree with the single slit pattern.
  • We get a central fringe of maximum intensity, and all other fringes of decreasing intensity, but of the same width as the central fringe. 
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13.6 Diffraction (cont)

     (http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/imgpho/dslit.gif)

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13.7 The Diffraction Grating

  • A diffraction grating consists of a plate with many closely spaced parallel slits ruled on it.
  • When a parallel beam of monochromatic light is diffracted normally at a diffraction grating, light is transmitted in certain directions only.
  • This is because the light passing through each slit is diffracted, and the diffracted light waves from adjacent slits reinforce eachother in certain directions only and cancel out in all other directions. 
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13.7 The Diffraction Grating (cont)

  • The central beam, called the zero order beam, is in the same direction as the incident beam.
  • The other transmitted beams are numbered outwards from the zero order beam.
  • Again, the angle of diffraction simply depends on how much diffraction is taking place.
  • More diffraction if: greater wavelength, smaller slit spacing. 
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13.7 The Diffraction Grating (cont)

  • d x sin (angle of diffraction) = n x wavelength.
  • where d = grating spacing, n = number of orders.
  • maximum diffraction is at 90 degrees, sin 90 = 1, so the maxiumum number of orders is given by d / wavelength, rounded down to the nearest whole number. 
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13.7 The Diffraction Grating (cont)

  • d x sin (angle of diffraction) = n x wavelength.
  • where d = grating spacing, n = number of orders.
  • maximum diffraction is at 90 degrees, sin 90 = 1, so the maxiumum number of orders is given by d / wavelength, rounded down to the nearest whole number. 
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13.7 The Diffraction Grating (cont)

  • d x sin (angle of diffraction) = n x wavelength.
  • where d = grating spacing, n = number of orders.
  • maximum diffraction is at 90 degrees, sin 90 = 1, so the maxiumum number of orders is given by d / wavelength, rounded down to the nearest whole number. 
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