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Optics. Introduction. Geometrical Optics Physical Optics Modern Optics Fundamental of Light Wave Description E ( r ,t) = A ( r )cos[ ω t – kr ] or E ( r ,t) = A ( r )e -i[ ω t – kr ] Velocity of propagation Intensity Wavelength and spectrum For visible light: 390 ~ 760 nm.
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Introduction • Geometrical Optics • Physical Optics • Modern Optics • Fundamental of Light Wave • Description E(r,t) = A(r)cos[ωt –kr] or E(r,t) = A(r)e -i[ωt –kr] • Velocity of propagation • Intensity • Wavelength and spectrum For visible light: 390 ~ 760 nm
Huygen’s Principle • Each point in a wave surface is a secondary source of waves, emitting secondary waves (wavelet) • A new wave surface is tangent to all secondary waves • Light rays are directed lines that are always perpendicular to the surface occupied by the disturbance at a given time and point along the direction of its motion
Reflection and Refraction of Plane Waves • Direction of all waves are all in one plane • Incident Angle = Reflection Angle • Snell’s law sin θi /sin θr = n21 Or n1 sin θi = n2 sin θr where n = c/v is the index of refraction of a given medium
Reflection and Refraction of Spherical Waves • A spherical wave fall on a plane surface, the reflected waves are spherical and symmetrical • The refracted wave are not spherical, and the refracted rays intersect at several points along the surface normal
Wave Geometry • Elaborate the phenomena of reflection and refraction from the geometrical point of view • The process are only reflections and refractions and no other changes occur at the wave surface • The geometrical treatment is adequate so long as the surfaces and other discontinuity are very larger compared with the wavelength
Image Formation of a Pinhole Camera • When the size of hole d is sufficiently small, a good image is formed • When d is large, the image is blurred • When d is too small such that it is comparable with the wavelength, the image is affected by the diffraction effect
Reflection at a Spherical Surface • Decartes’ formula for reflection at a spherical surface 1/p + 1/q = 2/r • Focus and focal length f = r / 2 • Concave and convex surfaces • Spherical aberration
Refraction at a Spherical Surface • Decartes’ formula for refraction at a spherical surface n1/p – n2/q = (n1 – n2 )/r • Object focus and image focus fo = r * n1/(n1 – n2) fi = -r * n2/(n1 – n2)
Example A concave surface whose radius is 0.5 m separates a medium whose index of refraction is 1.2 m from another whose index is 1.6. An object is placed in the first medium at 0.8 m from the surface. Determine the focal lengths, the position of the image, and magnification.
Lenses • A lens is a transparent medium bounded by two curved surfaces • Decartes’ formula for a thin lens 1/p – 1/q = (n – 1) * (1/r2 – 1/r1) • Object focal length 1/f = (n – 1) * (1/r2 – 1/r1) • Convergent and divergent lenses • Spherical aberration • Magnification M = q / p
Example A spherical lens has two convex surfaces of radii 0.8 m and 1.2 m. Its index of refraction is n = 1.5. Find its focal length and the position of the image of a point 2.0 m from the lens.
Optical Instrument • Magnifying glass M = q / f • Microscope M = δL/ff’ • Telescope Angular magnification M = f / f’ Resolving power β = 1.22 λ / D Where D is the diameter of objective lens
The Prism • A medium bounded by two plane surfaces making an angle (A) • Minimum value of deviation satisfies i = (δmin + A) / 2 Where i is the incident angle and δmin is the minimum value of deviation
Dispersion • Dispersion Medium index of refraction depends on frequency • Dispersion Each component wavelength will be refracted through a different angle • Dispersion in a Prism D = dδ / dλ = dδ / dn * dn / dλ D = 2 sin(A/2) / cos([δmin + A] / 2) * (-2B/λ3 )
Fermat’s Principle • In traveling from one point to another the ray choose the path for which the propagation time has a minimum value • Reflection at spherical surface
