Phys-272 Lecture 22

1 Phys-272 Lecture 22. Wave Propagation Reflection Refraction Phys-272 Lecture 22. Reflection Refraction Huygen's Principle Dispersion Light Scattering Polarization i = r n1 sin 1 = n2 sin 2. Index of Refraction (n). Speed of light, c, in vacuum is 3x108 m/s ( m/s). Speed of light, v, in a medium can be lower v < c. index of refraction, n = c/v frequency, f, is unmodified as v = f l, wavelength, l, depends on medium, = vT = v/f = c/nf = 0/n In some media, n, depends on f, this is called dispersion. Waves, wavefronts, rays Plane waves moving in +x direction r E ( x, y, z , t ) = E0 y cos(kx t ). r B( x, y, z , t ) = B0 z cos(kx t ). Wavefront is a surface of constant phase E field wavefront (y-z plane surface of constant phase). y Ray propagation x z Huygen's Principle Huygen's principle; a wave front can be a source of secondary wavelets that spread out in all directions at the speed of propagation in the medium. The envelope of leading edges forms a wave front.

2 This principle was stated by Huygen in 1678, it can be derived from Maxwell's eqns. It is a geometrical description of ray propagation. vt Plane wave example;. Secondary wavelets create another wave front (plane). Reflection from Huygen's Principle Consider wave fronts, separated by vt, the incident wave fronts in contact with the surface will create a wavelets according to Huygen's Principle and leds to another reflected wave front. Result is qi = qr reflected wave front Incident wave front vt vt vt ray diagram vt qr qi qi qr qi = qr Reflection Law The same effect can be seen with water waves in a ripple tank Refraction from Huygen's Principle Now the speed changes, from medium a to medium b, so the Speed may change and the wavefront spacing differs. L sinqa = vat = ct/na vat L sinqb = vbt = ct/nb n t vat e fro a v Medium a, va=c/na W. L L qa qb vbt vbt Medium b, vb=c/nb r ont avef W. na sinqa = nb sinqb same thing happens to marching soldiers Snell's Law What happens to the frequency ?

3 Nothing Snell's Law (law of refraction). normal Inc t ide n e fro nt av W. ra qa y Medium a, va=c/na qa Medium b, vb=c/nb qb Ref nt Angles are ef ro v defined ract Wa qb ted ef rac relative to the ed r R normal to plane y a na sinqa = nb sinqb Snell's Law Clicker question 2) A ray of light passes from air into water with an angle of incidence of 30o. Which of the following quantities does not change as the light enters the water.. a) Wavelength b) frequency c) speed of propagation d) direction of propagation. Material Index Indices of Refraction Vacuum Air at STP Polystyrene Ice Carbon disulfide Water at 20 C Flint glasses Acetone Heavy flint glass Ethyl alcohol Extra dense flint, EDF- Sugar solution(30%) 3. Methylene iodide Fluorite Sapphire Fused quartz Rare earth flint Glycerine Lanthanum flint Sugar solution (80%) Arsenic trisulfide glass Typical crown glass Diamond Crown glasses Spectacle crown, C-1 High Index n Lots of TIR.

4 Sodium chloride Clicker question Which of the following ray diagrams could represent the passage of light from air through glass and back to air? (nair=1 and nglass= ). (a) (b) (c). air air air glass glass glass air air air Clicker question Which of the following ray diagrams could represent the passage of light from air through glass and back to air? (nair=1 and nglass= ). (a) q1 (b) (c). air air air glass glass glass q2. air air air The behavior of these rays is determined from Snell's Law: n1 sin 1 = n2 sin 2. Since n(glass) > n(air), sinq (glass) < sinq (air) . Therefore, moving from air to glass, ray will bend toward normal. this eliminates (a). Moving from glass to air, ray will bend away from normal. this eliminates (c). As a matter of fact, the final angle in air must be equal to the initial angle in air!! qa EXAMPLE, from air into glass;. Suppose we have light in air (n=1). incidence on glass (n= ) at an angle qa=45 deg.

5 What is the angle qb of the refracted light, qb? nair sin a = n glass sin b (1) sin (45 ) = ( ) sin b ( ). (1) sin (45 ) 1. sin b = =. 2. b = 27 . EXAMPLE, from glass into air; qa Suppose we have light in glass (n= ). incident into air at an angle qa=30 deg. What is the angle of the refracted light, qb? qb n glass sin a = nair sin b ( ) sin (30 ) = (1) sin b sin b = ( ) sin (30 ) =. 2. b = 51 . Suppose you are stranded on a tropical island with no food. You see a fish in the water. Where should you aim your spear to hit the fish? ANSWER; do not aim directly at the apparent position of the fish. (Your spear will miss). Aim at the inside of the fish. Suppose in the previous question instead of a spear you had a high power laser to simultaneously kill and cook the fish (in the water). Where should you aim the laser?? ANSWER; aim directly at apparent fish position as the laser beam will refract to the correct fish position.

6 Total Internal Reflection Consider light moving from glass (n1= ) to air (n2= ). incident reflected sin 2 n1. ray ray = >1 2 > 1. n1 q1 qr GLASS sin 1 n2. n2 q2 AIR , light is bent away from the normal. refracted as q1 gets bigger, q2 gets bigger, but q2. ray can never get bigger than 90 !! In general, if sin q1 > (n2 / n1), we have NO refracted ray;. we have TOTAL INTERNAL REFLECTION. For example, light in water which is incident on an air surface with angle q1 > qc = sin-1( ) = will be totally reflected. This property is the basis for the optical fiber communication. Total Internal Reflection of a Laser Beam Material: PMMA. Endoscope used by physicians to look inside body. Clicker question I) The path of light is bent as it passes from medium 1 to medium 2. Compare the indexes of refraction in the two mediums. a) n1 > n2 Snell's Law: n1sinq1 = n2sinq2. Here, q2 >q1 implies n2 < n1. b) n1 = n2. c) n1 < n2. II) A light ray travels in a medium with n1 and completely reflects from the surface of a medium with n2.

7 The critical angle depends on: a) n1 only b) n2 only Critical angle occurs when q2 = 90o Therefore, sinqcritical = n2/n1. c) n1 and n2. Clicker question on Critical Angle . An optical fiber is Case I water n = surrounded by another dielectric. In case I this is glass n = qc water, with an index of refraction of , while in water n = case II this is air with an index of refraction of Case II air n = Compare the critical angles for total internal reflection glass n = qc in these two cases air n = a) qcI>qcII. b) qcI=qcII. c) qcI<qcII. Clicker question on Critical Angle . An optical fiber is Case I water n = surrounded by another dielectric. In case I this is glass n = qc water, with an index of refraction of , while in water n = case II this is air with an index of refraction of Case II air n = Compare the critical angles for total internal reflection glass n = qc in these two cases air n = a) qcI>qcII. n2. b) qcI=qcII n1 Since n1>n2 TIR will occur for q > critical angle.

8 Snell's law says sinqc=n2/n1. c) qcI<qcII n1>n2 If n2= , then qc is as small as it can be. So qcI >qcII . Total Internal Reflection Total internal reflection occurs when q>qc and provides 100%. reflection. This has better efficiency than silvered mirror. Examples of devices using Critical Angle Prism Binoculars Fiber Optics Fiber optics is extremely important for high speed Internet and digital data transfer at long distances. Many companies (Lucent, Oceanic Cable ) have laid fiber over long distances to provide internet service. Dispersion: n = n(w). The index of refraction depends on frequency, due to the presence of resonant transition lines. For example, ultraviolet absorption bands in glass cause a rising index of refraction in the visible, , n(higher w) > n(lower w): nred = nblue = Index of refraction white light ultraviolet absorption bands prism frequency Split into Colors Rainbows (how they form). Rainbow s Hence we also see a faint secondary rainbow 45o A meter stick lies at the bottom of a nwater = rectangular water tank of height 50cm.

9 You look into the tank at an angle of 45o relative to vertical along a line that skims the top edge of the tank. 50 cm What is the smallest number on the ruler that you can see? 0 20 40 60 80 100. Conceptual Analysis: - Light is refracted at the surface of the water Strategy: - Figure out the angle of refraction in the water and extrapolate this to the bottom of the tank. 45o A meter stick lies at the bottom of a nwater = rectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that qR. skims the top edge of the tank. 50 cm 0 20 40 60 80 100. If you shine a laser into the tank at an angle of 45o, what is the refracted angle qR in the water ? A) qR = B) qR = C) qR = nairsin(45) = nwatersin(qR). sin(qR) = nairsin(45)/nwater = qR = sin-1( ) = 45o A meter stick lies at the bottom of a nwater = rectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that qR.

10 Skims the top edge of the tank. 50 cm 0 20 40 60 80 100. qR = What number on the ruler does the laser beam hit ? A) cm B) cm C) cm 45o A meter stick lies at the bottom of a nwater = rectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that qR. skims the top edge of the tank. 50 cm 0 20 40 60 80 100. d qR = What number on the ruler does the laser beam hit ? A) cm B) cm C) cm tan(qR) = d/50. d = tan( ) x 50cm = 45o A meter stick lies at the bottom of a nwater = rectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that skims the top edge of the tank. 50 cm What is the smallest number on the ruler that you can see? 0 20 40 60 80 100. If the tank were half full of water, would the laser hit a bigger or a smaller number than it did when the tank was full of water ? A) bigger B) smaller C) The same number 45o 45o qR 45o 50 cm 50 cm d = cm d = 50 cm 0 20 40 60 80 100 0 20 40 60 80 100.