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IB Physics Option A: Sight and wave phenomena

The required material for the IB Physics Option A. Taken from the "First Examinations 2009" IB Physics Guide.

Rodolfo Alvarado

on 6 April 2013

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Transcript of IB Physics Option A: Sight and wave phenomena

IB Physics Option A:
Sight and wave phenomena A1 The eye and sight A2 Standing (stationary) waves A3 Doppler Effect A4 Diffraction A5 Resolution A6 Polarization A.1.1 Describe the basic structure of the
human eye. A.1.2 State and explain the process of depth
of vision and accommodation. A.1.3 State that the retina contains rods
and cones, and describe the variation
in density across the surface of the retina. A.1.4 Describe the function of the rods and
of the cones in photopic and scotopic
vision. A.1.5 Describe color mixing of light by
addition and subtraction. A.1.6 Discuss the effect of light and dark,
and color, on the perception of
objects. A.2.1 Describe the nature of standing
(stationary) waves. A.2.2 Explain the formation of
one‑dimensional standing waves. A.2.3 Discuss the modes of vibration of
strings and air in open and in closed
pipes. A.2.4 Compare standing waves and
traveling waves. A.2.5 Solve problems involving standing
waves. A.3.1 Describe what is meant by the
Doppler effect. A.3.2 Explain the Doppler effect by
reference to wavefront diagrams for
moving-detector and moving-source
situations. A.3.5 Solve problems on the Doppler effect
for electromagnetic waves using the
approximation A.3.3 Apply the Doppler effect equations
for sound. A.3.4 Solve problems on the Doppler effect
for sound. A.3.6 Outline an example in which the
Doppler effect is used to measure
speed. A.4.1 Sketch the variation with angle of
diffraction of the relative intensity of
light diffracted at a single slit. A.4.2 Derive the formula for the position of the first minimum of the diffraction pattern produced at a single slit. A.4.3 Solve problems involving single-slit
diffraction. A.5.1 Sketch the variation with angle of diffraction of the relative intensity of light emitted by two point sources that has been diffracted at a single slit. A.5.2 State the Rayleigh criterion for images of two sources to be just resolved. A.5.3 Describe the significance of resolution in the development of devices such as CDs and DVDs, the electron microscope and radio telescopes. A.5.4 Solve problems involving resolution. A.6.1 Describe what is meant by polarized light. A.6.2 Describe polarization by reflection. A.6.3 State and apply Brewster’s law. The structure should be limited to those features affecting the physical operation of the eye. The near point (25 cm) and the far point (infinity) of the eye for normal vision are also included. Students should be able to sketch and interpret spectral response graphs and give an explanation for color blindness. Students should be able to “identify” primary and
secondary colors. Students should consider architectural effects of
light and shadow (for example, deep shadow gives
the impression of massiveness). Glow can be used to give an impression of “warmth” (for example,blue tints are cold) or to change the perceived size of a room (for example, light-colored ceilings heighten the room). Students should consider energy transfer, amplitude and phase. Students should understand what is meant by nodes and antinodes. The lowest-frequency mode is known either as the fundamental or as the first harmonic. The term overtone will not be used. Problems will not include situations where both source and detector are moving. Students should appreciate that the approximation may be used only when v << c. Suitable examples include blood-flow measurements and the measurement of vehicle speeds. Diffraction at a single slit Students should sketch the variation where the diffraction patterns are well resolved, just resolved and not resolved. Problems could involve the human eye and optical instruments. This may be illustrated using light or microwaves. The use of polarized sunglasses should be included A.6.4 Explain the terms polarizer and
analyser. A.6.5 Calculate the intensity of a
transmitted beam of polarized light
using Malus’ law. A.6.6 Describe what is meant by an
optically active substance. A.6.7 Describe the use of polarization in the determination of the concentration of certain solutions. Students should be aware that such substances rotate the plane of polarization. A.6.8 Outline qualitatively how polarization may be used in stress analysis. A.6.9 Outline qualitatively the action of liquid-crystal displays (LCDs). A.6.10 Solve problems involving the polarization of light. Aim 8: The use of LCD screens in a wide variety of different applications/devices can be mentioned: laptops, calculators, cellphones, tablets, etc. Depth perception is the visual ability to perceive the world in three dimensions (3D) and the distance of an object. Accommodation is the process by which the vertebrate eye changes optical power to maintain a clear image (focus) on an object as its distance varies. The near point and far point are the locations that can be seen
without strain to the eye. Both are photoreceptors in the retina.
The rods are more sensitive than the cones. However, they are not sensitive to color. The cones provide the eye's color sensitivity and they are much more concentrated in the central spot. Photopic Scotopic Photopic vision is the vision of the eye under well-lit conditions. In humans and many other animals, photopic vision allows color perception, mediated by cone cells, and a significantly higher visual acuity and temporal resolution than available with scotopic vision. Scotopic vision is the vision of the eye under low-light conditions. In the human eye cone cells are nonfunctional in low light – scotopic vision is produced exclusively through rod cells which are most sensitive to wavelengths of light around 498 nm (green-blue) and are insensitive to wavelengths longer than about 640 nm (red). Spectral response graphs show the response of cones to color Color blindness or color vision deficiency is the inability or decreased ability to see color, or perceive color differences, under normal lighting conditions. There is no actual blindness but there is a deficiency of color vision. The most usual cause is a fault in the development of one or more sets of retinal cones that perceive color in light and transmit that information to the optic nerve. Color addition Color subtraction Created by mixing together light. Created by mixing together pigments. Primary colors:
Red, green, blue Secondary colors:
Cyan, magenta, yellow Primary colors:
Cyan, magenta, yellow Secondary colors:
Red, green, blue A standing wave is a wave that remains in a constant position. There is on average no net propagation of energy. The amplitude is fixed. Standing waves have constant phase. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. A wave can be reflected with a boundary and interfere with itself. The effect is a series of nodes (zero displacement) and anti-nodes (maximum displacement) at fixed points along the transmission line. Formulas from Topic 4: Oscillations and waves may be useful in some problems. It is the change in frequency of a wave (or other periodic event) for an observer moving relative to its source. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer.

The relative motion is the only thing that is necessary. So the source can be moving and the observer stationary or a stationary source and a moving observer. Moving-source Moving-detector The formulas for the frequency are: You can apply the formula to different situations: moving speaker, ambulance, person riding a bike in a circle, a person playing a violin on a train, etc. If the wavelength/frequency change is known the speed can be obtained. Students should know that the criterion for a circular aperture is The Rayleigh criterion for resolving two sources states that they can be just resolved if the first minimum of one source is at the same angle as the maximum of the other. Electron microscopes and radio telescopes depend on good resolution to get good data. The same applies to recording data or images.

Resolution of optical instruments can be improved by increasing the lens diameter. Polarization is a property of waves that can oscillate with more than one orientation. Electromagnetic waves, such as light, exhibit polarization.

It is described by specifying the orientation of the wave's electric field at a point in space over one period of the oscillation. When light travels in free space, in most cases it propagates as a transverse wave—the polarization is perpendicular to the wave's direction of travel. In this case, the electric field may be oriented in a single direction (linear polarization), Sunglasses or sun glasses are a form of protective eyewear designed primarily to prevent bright sunlight and high-energy visible light from damaging or discomforting the eyes. They can sometimes also function as a visual aid, as variously termed spectacles or glasses exist, featuring lenses that are colored, polarized or darkened. Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. This equation is known as Brewster's law, and the angle defined by it is Brewster's angle A polarizer is an optical filter that passes light of a specific polarization and blocks waves of other polarizations. It can convert a beam of light of undefined or mixed polarization into a beam with well-defined polarization. Malus' law says that when a perfect polarizer is placed in a polarized beam of light, the intensity, I, of the light that passes through is given by If two polarizers are placed one after another (the second polarizer is generally called an analyzer), the mutual angle between their polarizing axes gives the value of in Malus' law. If the two axes are orthogonal, the polarizers are crossed and in theory no light is transmitted. If a transparent object is placed between the polarlizer and analyzer, any polarization effects present in the sample will be shown as an increase in transmission. This effect is used in polarimetry to measure the optical activity of a sample. If the solution is optically active (changes the plane of polarization) to different degrees at different concentrations then you can use this to determine the concentration of the solution. You will just need to use a protractor to measure the angle difference. Light reflected is polarized by reflection. Stress alters the polarization of light passing through. So you can use polarization to do stress analysis. You can build a model of an object with perspex, then pass light trough crossed polarizers with the object in between. Stressed color regions will be seen. The color depends on the degree of stressing because in perspex the stress causes the rotation of polarization . LCDs use polarization to prevent light from reflecting on the screen and to the generate the required images. The Liquid crystal layer changes the direction of the polarization. Standing waves Travelling waves Energy is not propagated Energy is propagated Can have any frequency/wavelength Only specific wavelengths and frequencies Has nodes and antinodes Doesn't have nodes nor antinodes Constant phase Phase varies with position Amplitude is constant with position,
the amplitude varies if you change
position. Amplitude is the same for all points If the conditions are met we get resonance (loudest vibration possible by the system). These are called the boundary conditions. What is the wavelength of a standing wave if the distance between adjacent nodes is 5 cm? A = 10 cm

Additionally the frequency is 100 Hz ¿What is the speed of the wave?
A = 1000 m s -1 Muscles change the shape of the lens in the eye.

For far objects the lens is thicker and for near objects the lens is thinner. The two eyes see two slightly different views. Using the two different images the brain is able to determine depth. The intensity is halfed if a polarizer filters unpolarized light (independent of angle). If a polarizer filters polarized light then the intensity will go from no change to 0 according to the angle. Using the small angle
approximation sin(a) = a Where lambda is the wavelength, b is the aperture. Theta is the position (radians) On the diagram below, the path difference is lambda/2 for a minimum (total destructive interference for waves with same phase). sin(theta) = lambda/b. Determine the wavelength of light given that the first minimum on the diffraction pattern generated by a single slit appears 2 radians from the center and the aperture is of 350 nm. A = 700 nm. The aperture of the orbiting Hubble Space Telescope has a diameter of 3.00 m. What is the angle between two just-resolvable stars? Assume an average light wavelength of 500 nm.
A = 2.03 x 10 radians

Theta is the minimum separation between the two maxima so the images are resolved. The smaller the theta the more resolution the device has. -7 A speaker generates a 200 Hz sound.
An observer is riding a bike towards the speaker at 5 m s . Assume the speed of sound in air is 300 m s .Calculate the frequency perceived by the observer.
A = 203 Hz -1 -1 Vertically polarized light with intensity "I" passes a polarizer that is at a 30° angle. Calculate the intensity of the resulting light.
A = (3/4) I

Calculate the polarization angle of glass given that the light passes from air to glass with refractive index of 1.5
A = 56° Warm/Cold
Colors are perception Light/Dark
Space/ Massiveness Moving objects also shift the perceived frequency of electromagnetic waves. Lower frequencies are shifted more. n is the refractive index of the material, the angle is Brewster's angle Theta is the angle difference. Lambda is the wavelength and b is the aperture size c is the speed of light
v is the relative velocity v is the speed of sound in the medium
u is the speed of the observer/source
f prime is the perceived frequency.
f is the generated frequency.
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