Optics

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 = n 21 sin θi /sin θr = n 21 Or n 1 sin θi = n 2 sin θr Or n 1 sin θi = n 2 sin θr where n = c/v is the index of refraction of a given medium 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 n 1 /p – n 2 /q = (n 1 – n 2 ) /r  Object focus and image focus fo = r * n 1 /(n 1 – n 2 ) fi = -r * n 2 /(n 1 – n 2 )

Sign Conventions for a Spherical Refracting Surface + - Radius r ConcaveConvex Focus fo ConvergentDivergent Object p RealVirtual Image q VirtualReal

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/r 2 – 1/r 1 )  Object focal length 1/f = (n – 1) * (1/r 2 – 1/r 1 ) 1/f = (n – 1) * (1/r 2 – 1/r 1 )  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 = (δ min + A) / 2 Where i is the incident angle and δ min is the minimum value of deviation Where i is the incident angle and δ min 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 = dδ / dλ = dδ / dn * dn / dλ D = 2 sin(A/2) / cos([δ min + A] / 2) * (-2B/λ 3 ) D = 2 sin(A/2) / cos([δ min + A] / 2) * (-2B/λ 3 )

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