Electromagnetism and Light

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1 Electromagnetism and Light Monday Properties of waves (sound and light) interference, diffraction [Hewitt 12] Tuesday Light waves, diffraction, refraction, Snell's Law. [Hewitt 13, 14] Wednesday Lenses, polarization [Hewitt 14] Thurday/Friday Magnetic fields, forces and induction [Hewitt 11]

2 WEDNESDAY Diffraction limits, telescopes and laser weapons. Doppler effect Refraction and total internal reflection. Application to lenses and mirrors. Afternoon Lenses and images.

3 This lecture will help you understand: Reflection Refraction Dispersion Total Internal Reflection Lenses Polarization

4 Properties of Light I will love the light for it shows me the way. Yet I will endure the darkness for it shows me the stars. Og Mandino

$Single slit interference leads to Diffraction limit Destructive Condition slit: asin θ=mλ θmin$

5 Single slit interference leads to Diffraction limit Destructive Condition slit: asin θ=mλ θmin λ/a For circular aperture Theta is full width θmin 1.22 λ/d To see a 100 kly galaxy 2 M Ly away

6 Very Large Array min=1.22 D m/s = Hz 0.1 m 4 min=1.22 =10 rad 1220m

7 Air-borne laser, laser missile defense =2.8 m min=1.22 D

8 Death Star Large Mirror Good for destroying planets! min=1.22 D

Doppler Effect change of frequency due to the motion of the wave source most evident in change of pitch frequency of waves increases as the siren

9 Doppler Effect change of frequency due to the motion of the wave source most evident in change of pitch frequency of waves increases as the siren approaches (hear higher pitch) frequency of waves decreases as siren moves away (hear lower pitch) (Nice animations)

10 CLICKER QUESTION When a fire engine approaches you, the A. speed of its sound increases. B. frequency of sound increases. C. wavelength of its sound increases. D. all of the above increase

11 CHECK YOUR ANSWER When a fire engine approaches you, the A. speed of its sound increases. B. frequency of sound increases. C. wavelength of its sound increases. D. all of the above increase Comment: Be sure you distinguish between sound speed, and sound frequency.

12 Doppler Effect Doppler effect also applies to light increase in light frequency (blue shift) when light source approaches you decrease in light frequency (red shift) when light source moves away from you The expansion and the age of the Universe is entirely measured by the Doppler Effect. v=h*d v= speed of galaxy relative to Earth H= Hubble constant D=distance to galaxy

13 CLICKER QUESTION Doppler Effect The panel on the left are spectral lines from the sun. The panel at right are spectral lines of a distant star. The star is [A] A different composition of gasses as our sun [B] Moving away from Earth [C] Moving toward Earth [D] Not enough information.

14 CHECK YOUR ANSWER Doppler Effect The star is [A] A different composition of gasses as our sun [B] Moving away from Earth [C] Moving toward Earth [D] Not enough information. Explanation: The lines are in correct relative orientation, so are same gasses, but they move into the red. Thus star is moving away.

15 Index of refraction nmaterial= c vmaterial The change in speed at a material interface causes the light to bend (refract)

16 Definitions in Snell's law n1 sin 1 =n2 sin 2

17 n1 sin(θ1)=n2 sin(θ2)

18 n1 sin(θ1)=n2 sin(θ2) Dispersion Means n depends on λ.

19 Note that wavelength gets shorter going from deeper to shallower water Refraction is CAUSED by the change of speed as light goes from one medium to another.

$Once you see that refraction is caused by a speed change, you can$

20 Once you see that refraction is caused by a speed change, you can understand that it happens with light, sound, water and geologic waves.

21 CLICKER QUESTION Based on the values of n you just saw, which color of light travels slowest in water A. Red B. Green C. Blue D. White

22 CHECK YOUR ANSWER Based on the values of n you just saw, which color of light travels slowest in water A. Red B. Green C. Blue it had the highest index of refraction and v=c/n D. White

23 Problem A laser is fired under water and at an angle of 60 degrees from the normal. What angle does it make when it emerges into the air?

24 2=? 1=60 o

25 The math tells you the physics is funny n1 sin 1 =n2 sin sin 60 =1.33 sin =sin 2 2=? If angle greater than critical angle, then sin(theta2) > 1. Try arcsin(1.15) in your calculator.

26 Total internal reflection n2 sin(θc)= n1

27 Beyond the critical angle Beyond the critical angle there can be no transmitted ray. All is reflected. Applications: Fiber optic communications Pretty sculptures and clothing. Light guides (for surgery or caving)

28 Beyond the critical angle

29 Geometrical Optics '= s s f s' m= s R f= 2 n 1 Relation between object and image distance for single lenses and mirrors. Magnification for single lens or mirror. Lensmaker's formula bi convex or bi concave

30 Focal point Focal point: The point at which parallel rays converge. Focal length: f = distance to focal point.

31 Focal point of a mirror Use the law of reflection to show that the parallel rays all focus to the same point. The blue lines are normals

$Refraction at a curved surface R n R f=$

32 Refraction at a curved surface R n R f= (n 1) Plano convex lensmaker's equation

33 Converging and Diverging R f= (n 1) If the lens is thicker in the middle than the edges, (top row) it is converging. If thinner, (bottom row) diverging. R is said to be negative for concave lenses.

34 Bi vs. Plano R f Plano = n 1 If both surfaces of lens are curved it focuses twice as well so f is shorter. R f Bi= 2 n 1

35 Clicker Question You have two plano convex lenses that appear identical. One is made of glass with n=1.5. One is made of cubic zirconia with index n=2.2. (A) The glass lens has a longer focal length than the diamond lens. (B) Both lenses have the same focal length, because they are the same shape. (C) The diamond lens has a longer focal length because diamonds scatter light more than glass. (D) Not enough information given.

36 Ray Tracing with Lenses: The principal rays P ray: Ray parallel to symmetry axis goes thru focal point F. F ray: Ray thru F comes out parallel to symmetry axis M ray: Ray through middle of lens passes straight thru unchanged.

37 Image position and magnification = f s s' s' m= s s = distance to object s' = distance to image f = focal length m = magnification

38 Example: A convex lens Given a convex lens with focal length f = 5 cm. An object is placed 15 cm from the lens. Where is the image? What is the magnification? What if the object is placed 25 cm from a lens with focal length 10 cm?

39 Clicker Question Given an object placed 20 cm from a lens with focal length 10 cm, find the distance of the image from the lens (and the magnification M). (A) 5 cm, (B) 10 cm, (C) 20 cm, (D) 30 cm, M= -1/2 M= -1 M= -2 M= -3

40 phet phet.colorado.edu/en/simulation/geomet ric optics

41 Pinhole camera No lens needed!

44 Real and virtual images. Rays meet at a real image. Focus a flame and it will burn. Real images are on opposite side of lens (and same side of mirror) from object. Virtual images are on same side of les (and opposite side of mirror) from object. Real images are inverted, virtual are erect.

45 Example, a convex mirror Given a convex mirror with focal length f = 10 cm. An object is placed 15 cm from the mirror. Where is the image? What is the magnification? What if the object is placed 5 cm from the mirror?

46 Example, a concave lens Given a concave lens with focal length f = 10 cm. An object is placed 15 cm from the lens. Where is the image? What is the magnification? What if the object is placed 5 cm from the lens?

47 Clicker Question Given an object placed 20 cm from a biconcave lens with focal length magnitude 10 cm, find the magnification of the image (A) M= 20/3 (B) M= 1/2 (C) M= 1/3 (D) M= 3 (E) M=-1/2

48 Polarization Unpolarized light vibrations producing light are in random directions example: incandescent lamp, fluorescent lamp, candle flame

49 Polarization Polarized light Unpolarized light divided into two internal beams polarized at right angles to each other. One beam is absorbed while the other beam is transmitted.

50 Polarization CHECK YOUR NEIGHBOR Polarization occurs for waves that are A. transverse B. longitudinal. C. both A and B D. neither A nor B

51 Polarization CHECK YOUR ANSWER Polarization occurs for waves that are A. transverse B. longitudinal. C. both A and B D. neither A nor B

52 Wave Barriers and Bow Waves Wave barrier waves superimpose directly on top of one another producing a wall example: bug swimming as fast as the wave it makes

53 Wave Barriers and Bow Waves Supersonic aircraft flying faster than the speed of sound Bow wave V shape form of overlapping waves when object travels faster than wave speed an increase in speed will produce a narrower V shape of overlapping waves.

54 Shock Waves and the Sonic Boom Shock wave pattern of overlapping spheres that form a cone from objects traveling faster than the speed of sound

55 Sonic Boom Shock wave consists of two cones a high pressure cone generated at the bow of the supersonic aircraft a low pressure cone that follows toward (or at) the tail of the aircraft it is not required that a moving source be noisy Why does the air condense?

56 Cerenkov Radiation and Tachyons Particles traveling faster than light make a shock wave too! Fast charged particles in the water bath of a nuclear reactor make a blue glow. Tachyons would glow in a vacuum

57 Hewitt Problem 5 An electric field does 12 J of work on a charge of C as it moves from point A to point B. What is the voltage change between point A and point B? How much work does this same field do on a charge of Coulombs?

Electromagnetism and Light

Electromagnetism and Light Monday Properties of waves (sound and light) interference, diffraction [Hewitt 12] Tuesday Light waves, diffraction, refraction, Snell's Law. [Hewitt 13, 14] Wednesday Lenses,