Fa ‘04 Hopkins Chapter 19: Models of Light Particle Model of Light – Isaac Newton, in the mid 1600’s Wave Model of Light – mid to late 1800’s – lots of people – Huygens Wave-Particle Model – early 1900’s – combines the two ideas Our understanding of light is still incomplete – neither “wave” nor “particle” is correct – we lack the vocabulary to fully describe light properly

Fa ‘04 Hopkins Wave Refraction and Reflection In the wave model of light, all parts of a light beam are “interconnected” For reflection, the speed of the wave does not change after reflection from the boundary. For transmission, the wave front is bent at the interface because (as shown) the wave travels more slowly in the second medium (in this case).

Fa ‘04 Hopkins Particle vs Wave for Refraction A particle of light is incident on the boundary between two media. ii rr Huygens Principle is an alternate explanation and predicts a slower speed in second medium Huygens Explanation: For transmission, the wave front is bent at the interface because (as shown) the wave travels more slowly in the second medium Particle theory predicts greater speed in 2 nd medium

Fa ‘04 Hopkins Speed of Light in a Medium We know that light travels at 300,000 km/s in vacuum. In any other medium, it travels SLOWER. We describe this phenomenon in terms of the INDEX OF REFRACTION of the medium: Air: 1.000, Water: 1.33 Glass: 1.5, Diamond: Cubic Zirconia: 2.21

Fa ‘04 Hopkins Snell’s Law of Refraction ii ii rr Speed = v1 Speed = v2 Index of Refraction: n = c / v = n 1 sin(  i ) n 2 sin(  r )

Fa ‘04 Hopkins n water = 1.33 n air = 1.00 Special Case – Total Internal Reflection Light bends toward the normal as it passes from one medium into another more optically dense medium. The reverse is true as well, light bends away from the normal as it passes from a more dense to less dense medium. In such cases there is an angle of incidence for which the angle of refraction is 90 o. This is known as the Critical Angle cc  r =90 sin  1 / sin  2 = n 2 / n 1 sin  c / 1 = 1.00/ 1.33  c = o

Fa ‘04 Hopkins Total Internal Reflection - Applications Diamond: n = Critical Angle = degrees Almost all light entering top face is reflected back inside!!! Optical Fibres for Transmission of Light

Fa ‘04 Hopkins How a Prism Works Longer Wavelengths (i.e Red) have smaller index of refraction than shorter (i.e. Blue). Smaller index of refraction means it refracts LESS

Fa ‘04 Hopkins Rainbows!!!

Fa ‘04 Hopkins Light as a Transverse Wave During the 1800's there was growing evidence that light may indeed be a wave phenomena contrary to the beliefs of Isaac Newton. One piece of evidence was supplied by Thomas Young who showed that light demonstrated the wave property of interference.

Fa ‘04 Hopkins Polarization of Light During the 1800's and possibly even during Newton's time there was evidence that particular materials, such as iceland spar, could polarize a ray of light.

Fa ‘04 Hopkins How to polarize light By absorption By preferred transmission and reflection

Fa ‘04 Hopkins Applications of Polarization Astronomy: studying the polarization state of light from stars, galaxies, nebulae etc. can be used to map magnetic fields either around stars, or within the sun. Quantum theory: Many of the foundational problems in quantum theory can be studied using polarized light, e.g. The EPR paradox. Chemistry and biology: We've seen how different materials can affect polarized light. Thus, studying these effects can yield a large amount of information about molecular and atomic structure. Commercial applications: e.g. Liquid crystals: Birefringent molecules which can easily be re-oriented due to the application of an electric field. Twisted nematic cell. Used for amplitude modulation. This is the type of liquid crystal most commonly seen in watches, calculators, LCTVs etc.

Fa ‘04 Hopkins Summary Light exhibits both particle-like and wave-like properties Light can travel in a vacuum (particle) Light travels slower in a medium than in vacuum (mostly wave) Light reflects (both) Light refracts (mostly wave) Light interferes (wave) Light is polarizable (wave)

Fa ‘04 Hopkins Converging and Diverging Lenses For the convex lens shown, any parallel rays of light that enter the lens will pass through the focus on the right (f is positive). c c ff For a concave lens parallel rays diverge and appear to come from the focus behind the lens (f is negative) c c ff

Fa ‘04 Hopkins Convex Lenses Three principle rays can be drawn. 1.Ray passes through geometric center of lens undisturbed 2.Parallel ray entering passes through focus 3.Ray passes through focus emerges parallel c c ff dodo didi hoho hihi

Fa ‘04 Hopkins Thin Lens Formula c c ff dodo didi hoho hihi Magnification Formula: Lens Formula:

Fa ‘04 Hopkins Thin Lens Formula c c ff dodo didi hoho hihi Object Side Image Side

Fa ‘04 Hopkins Sample Convex Lens An 30 cm object is placed 60 cm in front of a convex lens with a focal length of 24 cm. Describe the image. h o =30 60 hihi didi 1/f = 1/d o + 1/d i 1/24 = 1/60 + 1/d i 10/240 = 4/ /d i 1/d i = 6/240 d i = 40 m = -d i /d o = -40/60 = -.67 Object is real, smaller (20 cm), and inverted

Fa ‘04 Hopkins Concave Lens Example An object is place 60 cm in front of a concave lens with a focal length of 12 cm. Describe the image. 1/f = 1/d o + 1/d i -1/12 = 1/60 + 1/d i -5/60 = 1/60 + 1/d i 1/d i = -6/60 d i = -10 (neg sign indicates virtual image) m = -d i /d o = - -10/60 = Object is virtual, smaller, and upright h o =30 60 hihi didi