Essential Physics I: Reflection and refraction. Lecture 12:

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1 Essential Physics I: E Reflection and refraction Lecture 12:

Last lecture: review Fluids Hydrostatic equilibrium

F 2 A 2 volume flow rate Av = constant for liquid

2 Last lecture: review Fluids Hydrostatic equilibrium Archimedes Principal P 0 mg h P = P 0 + g h for liquid (constant ) Buoyancy: pressure force on object P = weight of fluid displaced P = F 1 A 1 = F 2 A 2 volume flow rate Av = constant for liquid (constant ) Bernoulli s equation P + gy v2 = constant

3 Last lecture: review A lead ball ( = 11.3g/cm 3 ) enters a tub of mercury ( = 13.6g/cm 3 ). What happens? (A) (B) (C) (D) Lead ball will float with ~ 83% of volume below mercury surface Lead ball will float with 100% of volume below mercury surface Lead ball will float with ~17% of volume below mercury surface Lead ball will sink

4 Last lecture: review A lead ball ( = 11.3g/cm 3 ) enters a tub of mercury ( = 13.6g/cm 3 ). What happens? (A) (B) (C) (D) Lead ball will float with ~ 83% of volume below mercury surface Lead ball will float with 100% of volume below mercury surface Lead ball will float with ~17% of volume below mercury surface Lead ball will sink

5 Last lecture: review A lead ball ( = 11.3g/cm 3 ) enters a tub of mercury ( = 13.6g/cm 3 ). What happens? V sub (A) Lead ball will float with ~ 83% of volume below mercury surface Archimedes Principal Buoyancy force = weight of mercury displaced = Hg V sub g Fe Hg = V sub V tot =0.83 = weight of lead ball = Fe V tot g

6 Last lecture: review You are driving a convertible car at 65 mph. The soft roof and windows are closed. The roof... (A) bows inward (B) Same as when car is stopped (C) bows outward (D) bows inward only when driving uphill (E) bows inward only when driving downhill

7 Last lecture: review You are driving a convertible car at 65 mph. The soft roof and windows are closed. The roof... (A) bows inward (B) Same as when car is stopped (C) bows outward (D) bows inward only when driving uphill (E) bows inward only when driving downhill

8 Last lecture: review You are driving a convertible car at 65 mph. The soft roof and windows are closed. The roof... (C) bows outward Bernoulli s equation P + gy v2 = constant lower constant air moving air not moving higher lower pressure pressure gradient, force P

9 Optics Reflection & Refraction

10 Optics Light is a wave: y(x, t) =A cos(kx ±!t) But, if light is interacting with an object much bigger than its wavelength: <<x Assume: Light travels in a straight line: a ray x Geometrical optics

11 Optics Huygen s principle Every point on a wavefront is the source of spherical propagating wavelets moving at the wave speed. The envelope of these wallets forms the next main wavefront.

$Refraction$

12 Reflection & Refraction Reflection Refraction

13 Reflection & Refraction Reflection: Light ray hits surface Ray moves away from surface Refraction: Light ray hits surface Ray enters object and changes direction.

14 Reflection & Refraction Usually, a ray is both reflected and refracted. medium 1 incident ray medium 2 refracted ray reflected ray

$Reflection & Refraction Your eye used both reflection and$

15 Reflection & Refraction Your eye used both reflection and refraction: light reflects off objects light refracts in our eye to form images

Reflection medium 1 1 0 1 0 1 = 1 medium 2 e.g.

16 Reflection medium = 1 medium 2 e.g. Au foil Specular reflection Parallel rays, smooth surface Rays reflected without distortion. e.g. white paper Diffuse reflection Rough surface Rays reflected in different directions

17 Reflection Example 2 mirrors joined at right angles (perpendicular) Show any incident light ray will return anti-parallel (opposite direction) turn 180 since 0 1 = 1

18 Reflection Example 2 mirrors joined at right angles (perpendicular) Show any incident light ray will return anti-parallel (opposite direction) turn 180 light ray turned by light ray turned by Total turning angle: (180 2 ) + (180 2 ) = 360 2( + )

19 Reflection Example 2 mirrors joined at right angles (perpendicular) Show any incident light ray will return anti-parallel (opposite direction) turn = 90 Total turning angle: (180 2 ) + (180 2 ) = 360 2( + ) 360 2(90 ) = 180

20 Reflection What is the angle? (A) 120 (B) (C) 65 (D) 55

21 Reflection What is the angle? = 55 (A) 120 (B) (C) 65 (D) = ( ) = 35

22 Reflection What is the angle? (A) 100 (B) 50 2 (C) (D) 120 Think carefully about angles!

23 Reflection What is the angle? (A) 100 (B) 50 2 (C) (D) 120

24 Reflection What is the angle? Sum up all the internal angles: (180 ) = ( )=

25 Reflection What is the angle? = = = = 90 (90 1 ) + (90 2 ) = = ( )= = 100

26 Partial Reflection Some reflection always occurs... even in glass Smallest reflection for an incident ray normal ( 90 ) to surface. Glass ~ 4% reflected light Larger angle results in more reflection

$Refraction 1 medium 1 medium 2 Refraction occurs when a$

27 Refraction 1 medium 1 medium 2 Refraction occurs when a light ray enters a new medium. It changes speed and direction

28 Refraction 1 medium 1 medium 2 Refraction occurs when a light ray enters a new medium. It changes speed and direction he speed of light in a transparent medium is lower than in a vacuum. c v v<c vacuum transparent media e.g. glass c = m/s speed of light in a vacuum (index of refraction) n = c v

$Refraction c v n = c v vacuum transparent media e.g.$

29 Refraction c v n = c v vacuum transparent media e.g. glass v = f = v f = c nf Neither c nor f change. 2 Only and n. / 1 n Each media must see same peaks/trough per time, so f is unchanged.

30 Refraction

31 Refraction The change in causes the direction to change: shared side sin sin 2

$Refraction The change in causes the direction to change: 1 1 2 1 sin 1 = 2 2$

32 Refraction The change in causes the direction to change: sin 1 = 2 2 sin 2 shared side and since: 1 = c f 1 n 1 n 1 sin 1 = n 2 sin 2 Snell s law

$Refraction n 1 sin 1 = n 2 sin 2 When going from low n.$

33 Refraction n 1 sin 1 = n 2 sin 2 When going from low n to high n the ray bends towards to the normal 2 When going from high n to low n the ray bends away to the normal 2

34 Refraction Example Show the ray exiting the glass slab is parallel to the incident ray. incident ray n 1 sin 1 = n 2 sin 2 Snell s law Refraction occurs: glass slab entering block: low n to high n 1sin 1 = n sin 2 sin 2 =sin 1 /n exiting block: high n to low n n sin 3 =1sin 4 sin 4 = n sin 3 slab faces parallel: 2 = 3 sin 4 = n sin 1 =sin 1 n rays are parallel!

$Refraction Example Laser reads a CD Beam enters a CD 0.$ Snell s law: n 1 sin 1 = n 2 sin 2 2 =sin 1 (n 1 sin 1 /n 2 ) = 17.

35 Refraction Example Laser reads a CD Beam enters a CD mm wide Refracted to width d mm CD thickness What is d? Snell s law: n 1 sin 1 = n 2 sin 2 2 =sin 1 (n 1 sin 1 /n 2 ) = d = D 2x = D 2t tan 2 =1.80µm Refraction allows a larger laser to be used for CD players

36 Refraction Rank the refractive indices. (A) (B) n 1 >n 2 >n 3 n 3 >n 1 >n 2 (C) n 3 >n 2 >n 1 (D) n 2 >n 1 >n 3

$Refraction Rank the refractive indices.$

37 Refraction Rank the refractive indices. (A) (B) n 1 >n 2 >n 3 n 3 >n 1 >n 2 (C) n 3 >n 2 >n 1 (D) n 2 >n 1 >n 3

38 Refraction What is? 50 (A) (B) n =1 n =1.53 (C) 50 (D) 60

39 Refraction What is? 50 (A) (B) n =1 n = (C) 50 Snell s law n 1 sin 1 = n 2 sin 2 (D) 60 sin 50 =1.53 sin 2 2 =sin 1 sin = 30 = 90 2 = 60

$refraction? Light is wave.$ $Reflection & refraction are interactions$

40 Brewster Angle There is a special angle, reflection occurs. p, where no p p Why? What is REALLY happening in reflection & refraction? Light is wave an electric (and magnetic) wave Reflection & refraction are interactions between the wave s electric field and atoms.

$dipole + - atom oscillates oscillation produces refracted$ wave Parallel to oscillation, there is no electric field =

41 ( Brewster Angle wave is absorbed by atom (actually a dipole + - atom oscillates oscillation produces refracted wave Parallel to oscillation, there is no electric field = no wave If reflected ray is in this direction, no reflection occurs!

42 Brewster Angle Brewster angle, p p p occurs when: p + 2 = = 90 p sin 2 = sin(90 p ) = cos p Snell s law: sin 2 = n 1 n 2 sin p p p 2 Therefore: tan p = n 2 n 1 p Air/glass interface: p = 56

43 Brewster Angle

44 Brewster Angle = Polarising Angle Normally, light is made from waves that oscillate in different directions: Same direction of motion,... = different oscillation directions E E E E E

45 Brewster Angle = Polarising Angle Normally, light is made from waves that oscillate in different directions: Same direction of motion,... = different oscillation directions If light only oscillates in one direction, it is polarised E E E E E

46 Brewster Angle = Polarising Angle Normally, light is made from waves that oscillate in different directions: Same direction of motion,... = different oscillation directions If light only oscillates in one direction, it is polarised p p Non-polarised light at the Brewster angle reflects polarised light: 90 only light component with oscillations perpendicular to atom oscillation.

47 Brewster Angle Find the refractive index of a material with a Brewster (polarising) angle in air of. 62 (A) 1.5 (B) 1.0 (C) 1.9 (D) 1.7

48 Brewster Angle Find the refractive index of a material with a Brewster (polarising) angle in air of. 62 (A) 1.5 (B) 1.0 n 2 = n 1 tan p =(1.0) tan(62 )=1.9 (C) 1.9 (D) 1.7

49 Total Internal Reflection How does this happen? How can we trap light in a clear tube?

$If the angle of refraction > 90, total internal reflection occurs.$

50 Total Internal Reflection Light moving from medium with high n to low n is bent away from the normal. If the angle of refraction > 90, total internal reflection occurs. Light cannot escape the glass. The incident ray s critical angle is when the angle of refraction = 90 n 1 sin 1 = n 2 sin 2 n 1 sin c = n 2 sin 90 sin c = n 2 n1

51 Total Internal Reflection

52 Total Internal Reflection The glass prism has n = 1.5 and is surrounded by air (n = 1). What would happen to the incident light ray if the prism were immersed in water (n =1.333)? (A) Most would exit into the water through the diagonal face and some would be reflected. (B) Most would be reflected and some would exit into the water through the diagonal face.

Total Internal Reflection The glass prism has n = 1.5 and is surrounded by air (n = 1). What would happen to the incident light ray if the prism were immersed in water (n =1.333)?

53 Total Internal Reflection The glass prism has n = 1.5 and is surrounded by air (n = 1). What would happen to the incident light ray if the prism were immersed in water (n =1.333)? (A) Most would exit into the water through the diagonal face and some would be reflected. (B) Most would be reflected and some would exit into the water through the diagonal face. sin c = n 2 n1 increase

54 Total Internal Reflection A whale s view Light rays in the red region are from objects above the water. Light rays outside red region are from objects in the water.

55 Total Internal Reflection Example A whale s view What is, the half-angle of the cone in which the whale sees above the water? c =sin 1 (1/1.333) = 48.6

Total Internal Reflection Information for the internet,

$The cladding has a lower refractive index, n Total internal$ reflection at core/cladding interface.

56 Total Internal Reflection Information for the internet, telephones and television is carried in optical fibres. Cable has glass core inside cladding. The cladding has a lower refractive index, n Total internal reflection at core/cladding interface. Lighter and more durable than copper wire. Two wires on right carry same rate of information! optical fibre copper wire

57 Total Internal Reflection What is the critical angle for light in a glass with n = 1.52 when the glass is immersed in water (n = 1.333). (A) 61.3 (B) 41.1 (C) 80.9 (D) none

58 Total Internal Reflection What is the critical angle for light in a glass with n = 1.52 when the glass is immersed in water (n = 1.333). (A) (B) c =sin 1 (n 2 /n 1 ) (C) 80.9 =sin 1 (1.333/1.52) = 61.3 (D) none

59 Total Internal Reflection What is the critical angle for light in a glass with n = 1.52 when the glass is immersed in benzene (n = 1.501). (A) 61.3 (B) 41.1 (C) 80.9 (D) none

60 Total Internal Reflection What is the critical angle for light in a glass with n = 1.52 when the glass is immersed in benzene (n = 1.501). (A) (B) (C) c =sin 1 (n 2 /n 1 ) =sin 1 (1.501/1.52) = 80.9 (D) none

61 Total Internal Reflection What is the critical angle for light in a glass with n = 1.52 when the glass is immersed in diidomethane (n = 1.738). (A) 61.3 (B) 41.1 (C) 80.9 (D) none

62 Total Internal Reflection What is the critical angle for light in a glass with n = 1.52 when the glass is immersed in diidomethane (n = 1.738). (A) 61.3 n 1 (= 1.52) >n 2 (= 1.738) (B) 41.1 sin 1 (1.738/1.52) no solution! (C) (D) 80.9 none no total internal reflection for light moving in glass.

$Dispersion Refraction is the interaction between the light wave and the atoms.$

63 Dispersion Refraction is the interaction between the light wave and the atoms. It depends on the frequency of the wave The refractive index, wave frequency. n, depends on Different frequencies refract through different angles. This is dispersion.

64 Dispersion This is what causes prisms to separate white light into it s many parts, as each colour has it s own λ. Determines how a rainbow works!

Dispersion Dispersion can be bad: Lenses focus

65 Dispersion Dispersion can be bad: Lenses focus colours as different places. Chromatic aberration Dispersion in optical fibres. Rays take different paths by reflecting at different angles. Dispersion can be good: Measuring dispersion in the atmosphere allows GPS devices to correct for atmospheric conditions.

Light sources can be natural or artificial (man-made)

Light The Sun is our major source of light Light sources can be natural or artificial (man-made) People and insects do not see the same type of light - people see visible light - insects see ultraviolet