The Nature of Light The earliest (~1000 A.D.) description of light was that of a stream of tiny particles –Newton described light with a particle model as well Huygens described many properties of light successfully using a wave picture (1670) Young showed that light beams can interfere with one another (1801), giving strong support to wave theory Maxwell’s theory of electromagnetic waves included light (1865) Results of early 20 th Century physics experiments could only be explained using a particle picture of light

The Nature of Light Einstein explained the results of the photoelectric effect experiment using the concept of photons (1905) –The energy E of a photon is proportional to the frequency f of the electromagnetic wave h = Planck’s constant (a very small number) So what is light, a wave or a particle? Experiments show that it must be both! –But never both at the same time –A “wave-like” experiment will give wave-like results –A “particle-like” experiment will give particle-like results

The Ray Approximation Light travels in a straight-line path in a homogenous medium until it encounters a boundary between two different materials Thus light propagation can be approximated as rays drawn along the direction of travel of the light beam –Rays are perpendicular to the wave fronts –Wave fronts are nearly planar for light that is far from its source (“plane waves”)

Reflection When light reaches a boundary between 2 media, some of the light is reflected back into the incident media For specular reflection: Specular reflection (smooth surface) Diffuse reflection (rough surface) (Law of Reflection)

Refraction When light reaches a boundary between 2 transparent media, some of the light is reflected back and some is refracted (bent) into the other media –Angle of refraction =  2 –Light is bent either toward or away from the normal, depending on its relative speed in each medium

Refraction Think of a barrel rolling toward the interface between two unlike surfaces Refraction is responsible for being able to see objects that would otherwise be outside your field of view

Law of Refraction It is convenient to define an index of refraction, a constant, unitless number for a particular medium As light travels from one medium to another, its frequency does not change –Otherwise waves would “bunch up” or be created or destroyed at boundaries between different media –Since v = f, wavelengths must change at boundaries –Thus we have: v 1 = f 1 and v 2 = f 2 –Also: 1 n 1 = 2 n 2

Law of Refraction Thus wavelength of light gets smaller (larger) when it enters medium of larger (smaller) n Snell’s law of refraction: –Light refracts toward (away from) normal when n 1 n 2 ) –  1,  2 are measured with respect to the normal n 1 = 1.00 n 2 = 1.52 n 1 = 1.52 n 2 = 1.00

Example Problem #22.19 Solution (details given in class): cm Transmission Through 3 Media When the light ray passes through the glass block as shown, it is shifted laterally by a distance d. Find the value of d.

Example Problem #22.28 Solution (details given in class): 2.5 m A cylindrical cistern, constructed below ground level, is 3.0 m in diameter and 2.0 m deep and is filled to the brim with a liquid whose index of refraction is 1.5. A small object rests on the bottom of the cistern at its center. How far from the edge of the cistern can a girl whose eyes are 1.2 m from the ground stand and still see the object?

Applications of Reflection and Refraction The index of refraction depends on wavelength (dispersion) Thus the angle of refraction when light enters a material depends on its wavelength –Violet (  400 nm) deviates the most –Red (  650 nm) deviates the least –Principle behind the prism and formation of rainbows Max. angles 

Rainbows The Raindrop

Rainbows

Total Internal Reflection When light attempts to move from a medium with a higher index of refraction to one with a lower index of refraction, total internal reflection can occurtotal internal reflection –At some critical angle  c the refracted light ray moves parallel to the boundary –When  1 =  c,  2 = 90 ° and Snell’s law gives:

Application: Fiber Optic Cables Example of total internal reflection within solid glass or transparent plastic rods –Used to “pipe” light from one place to another with very little loss of light intensity –Used frequently by doctors as an imaging tool –Light can travel through bends or light “kinks” in rod without losses (N 1 > N 2 )

Example Problem #22.47 Solution (details given in class): (a)53.1° (b)38.7° The figure above shows the path of a beam of light through several layers with different indices of refraction. (a) If  1 = 30.0 °, what is the angle  2 of the emerging beam? (b) What must the incident angle  1 be in order to have total internal reflection at the surface between the medium with n = 1.20 and the medium with n = 1.00 ?

Interactive Example Problem: Snell’s Law and Total Internal Reflection Animation and solution details given in class. (PHYSLET Physics Exploration 34.2, copyright Pearson Prentice Hall, 2004)