Dispersion. f (increasing frequency)

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$Dispersion The index of refraction n is usually a property of the medium but equally important, it also$

1 Dispersion The index of refraction n is usually a property of the medium but equally important, it also varies with the frequency f of light dispersion. n typically increases with increasing f. f (increasing frequency)

2 Physical Observable Consequence of Dispersion The Visible Spectrum of White Light According to Snell s Law, angle of refraction depends on n, n angle of refraction sin nsin and nsin a fixed incident direction of white light blue n > n blue red red white light air glass a blue red

3 Dispersion by a Prism D prism

4 Dispersion in a Rainbow From a Single Drop Red comes out at 42 o Blue comes out at 40 o

5 Dispersion in a Rainbow Double Rainbow from Multiple Droplets Note: blue ray from this drop misses eye Gifs taken from

6 Polarization For a transverse wave on a string, the direction of the wave s displacement gives the polarization of the wave.

7 A Linearly Polarized EM Wave For an electromagnetic wave, the direction of the electric field vector gives the polarization of the wave. E ( x, t) An transverse electromagnetic wave with polarization in the y-direction: E( x, t) Emax cos( kxt)ˆj ( x, t) B ˆ B max cos( kxt) k A polarized wave in a well defined direction is called a linearly polarized wave.

8 Polarization by Filters A non-linearly polarized wave on a string can be polarized by a slot barrier. Polaroid Filter for an EM Wave

9 The Action of a Polarizing Filter Unpolarized incident light will be linearly polarized parallel to the polarizing axis after transmission. We can analyze the intensity of the transmitted light passing thru the second polarizer (an analyzer): Only E will be transmitted, E E Ecos trans

a polarizer For an upolarized light, E is in

10 The Action of a Polarizing Filter Since intensity (I) is proportional to E 2, I I trans cos 2 max (Malus s Law) Transmitted intensity of linearly polarized light through a polarizer For an upolarized light, E is in all directions, Itrans Imax cos Imax 2 0 D polarizer

11 Polarization by Reflection At the special angle (polarizing angle or Brewster s angle) p, the electric field component parallel to the plane of incidence will not be reflected! This occurs when 2 applet b p

12 Brewster s Angle Weblink

13 Polarization by Reflection From Snell s law, we have, Then, using the condition for p : 2 n n sin n sin a p b b sin n sin( 2 ) a p b p b p This gives n sin n cos a p b p tan p n b n a (Brewster s Law)

14 Polarization by Reflection tan p n b n a For water/air (1.33/1) interface, For glass/air (1.5/1) interface, p p (with polarizer to window plane) (with polarizer to window plane)

5/1) interface, p p 53 56 (with polarizer to

15 Polarization by Reflection tan p n b n a For water/air (1.33/1) interface, For glass/air (1.5/1) interface, p p (with polarizer to reflection plane) (with polarizer to reflection plane)

Circular and Elliptical Polarization An elliptical polarized wave resulted when we have the superposition of two linearly polarized EM waves.

16 Circular and Elliptical Polarization An elliptical polarized wave resulted when we have the superposition of two linearly polarized EM waves. In the special case when the two waves have equal amplitudes and are separated in phase by a quarter-cycle, a circular polarized wave will result. The resultant electric field vector E will appear to rotate in a circle. animation

17 Circular Polarization Weblink

Huygens Principle Christiaan Huygens (1629-195): The Huygens Principle can be used to

It is a geometrical construction using every point on a wave front as the source of

18 Huygens Principle Christiaan Huygens ( ): The Huygens Principle can be used to predict the spreading of light wave. It is a geometrical construction using every point on a wave front as the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave. Application to the Law of Reflection a

19 Huygens Principle Applies to Reflection normal direction of r reflected ray r r Since AQ OP QP90 AO AO AQO OPA and r a

20 Huygens Principle Applies to Reflection Since AQ OP QP90 AO AO AQO OPA and r a

21 Huygens Principle Christiaan Huygens ( ): The Huygens Principle can be used to predict the spreading of light wave. It is a geometrical construction using every point on a wave front as the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave.

$Refraction Note: Wave slow down in$ material b!

22 Huygens Principle Application to Refraction Note: Wave slow down in material b! Distance traveled by wave in b is shorter smaller wavelets

$Huygens Principle Application to Refraction In time t, the wavelet at Q travels to O and the wavelet at A travels to B.$

23 Huygens Principle Application to Refraction In time t, the wavelet at Q travels to O and the wavelet at A travels to B. QO vat AB vbt Using AQO and OBA, we have, vt a sina AO vt b sinb AO Substituting v c n and v c n and dividing, a a b b sin cn n sin cn n a a b b b a n sin n sin a a b b (Snell s Law)

Chapter 1 - The Nature of Light

Chapter 1 - The Nature of Light David J. Starling Penn State Hazleton PHYS 214 Electromagnetic radiation comes in many forms, differing only in wavelength, frequency or energy. Electromagnetic radiation comes in many forms, differing