Physics 30 Light Unit Handouts

Warriors’

Physics 30 Light Unit

Handouts

I Is it a Wave or a Particle?

 Straight Lines, Crossed Theories + Law of Reflection

 Curved Mirrors and Ray Diagrams

 Law of Refraction + Lenses

 Searching for Diffraction and Interference

 Speed Experiments

II Modern Theories

 Maxwell’s Illuminating Insight

 Planck’s first Plank

 Einstein’s Explanation

 Compton’s Essential Duality

Straight Lines, Crossed Theories

1. Name 2 pieces of evidence that shows light travels in straight lines.

2. What would destructive interference look like for light?

3. Complete this diagram of a pinhole camera pointed at a candle to convince a skeptic that light travels in straight lines.

·

4. Name the theorists responsible for the wave and particle theories?

Law of Reflection

5. Define the angle of incidence.

6. Use the law of reflection to determine the angle the ray will reflect off of the second mirror.

7. A light ray intersects a mirror with an angle of incidence of 40°, what is the angle between the reflected ray and the mirror?

8. A shoe sales person is attempting to determine the correct length of mirror required so a 2.20 m tall basketball player can see their shoes. Use the law of reflection to determine the minimum length of mirror this salesperson requires.

9. The sun is directly overhead and you are trying to use your plane mirror to signal to a rescue party which is on a hill 35° above the horizontal from your position. What angle should you hold your mirror at? Perhaps this diagram will help you…

150°

20°

sunlight

mirror reflected ray

Curved Mirrors and Ray Diagrams

1. Label these: principle axis, vertex, focus, centre of curvature

2. Complete these statements:

a. A ray traveling parallel to the principle axis will reflect out through the ____________.

b. A ray traveling in through the centre will reflect out through the _________________.

c. A ray traveling in through the focus will reflect out traveling ____________________.

3. Draw 2 rays for each of these objects and locate the image.

a

b

c

d

e.

f.

g.

4. Describe where the image moves when the object does the following:

a. starts at infinity and moves in towards the centre of curvature of a concave mirror b. starts at the centre and moves in towards the focus of a concave mirror.

c. starts at the focus and moves in towards the vertex of a concave mirror.

d. starts far from a convex mirror and moves in towards the vertex.

5. Look at the images you found in question 3 above and describe them:

a. real or virtual, b. erect or inverted,

c. calculate their magnification (-Hi/Ho)

Law of Refraction and Lenses

1. Why does light bend towards the normal when it enters a more dense medium according to the two theories of light?

2 a. Label: the angle of incidence, angle of refraction, normal line on the diagram below.

b. Show: the path of the refracted ray as it leaves the shaded region.

c. Is the shaded region high or low optical density?

3. A light ray is incidence at 17.0° on the boundary between air (n = 1.00) and a high index (n = 1.65) plastic from a pair of glasses The angle of refraction is _____ °.

Round and record your answer with 3 significant digits.

4. Calculate the index of refraction of a piece of window glass from which a ray of light incident at 23.0° refracts into water (n = 1.33) at 27.0°

5. Calculate the angle of refraction for a ray of light that enters a triangular equilateral glass prism (n = 1.40) with an angle of incidence of 30°

6. Calculate the critical angle, and identify the incident medium for the boundary of a. water (n = 1.33) and air (n= 1.00)

b. water (n = 1.33) and an 80% sugar solution (n = 1.49) 7. Use the wave model of light to calculate the speed of light in

a. air (n = 1.0003) b. water (n = 1.33) c. ice (n= 1.31) d. diamond (n = 2.42)

8. You will note that the crown and the pavilion of a diamond have characteristic shapes. This allows the diamond to sparkle – i.e. it causes most light to leave the diamond from the top. Explain how the shape causes the sparkle.

crown

pavilion

9. Use ray diagrams to locate the image and describe the image you drew (magnification, real/virtual, upright/inverted)

a.

b.

c.

d.

e.

10. Measure the focal length and the object distance above and then use the lens/mirror equation to confirm the position of the images you have drawn.

Searching for Diffraction and Interference

1. Use the principle of superposition to predict the results of these two waves meeting.

2a. Show on the diagram at right, where you measure x, d, n, and L in Young's double slit experiment.

b. Describe two ways in which x can be increased.

3. When 500 nm light (yellow) is shone through a diffraction grating that has 3.0 micrometers between the openings and onto a screen that is 80 cm from the grating how far will the second order antinode be from the central bright spot?

4. Bright spots are 2.5 cm apart on a screen 0.75 m from a diffraction grating that was manufactured with 6.5 x 10⁴ lines/m. What is the wavelength of the light being used?

5. CDs show the rainbow as a result of light diffracting from their pitted surface.

Students measured the distance between the pits by shining 640 nm red light on the surface and measuring the angle between the central bright line and the first order antinode to be 12°. What is the distance between the pits?

6. White light is shone through a diffraction grating with lines spaced at 2.00 x 10^-5 m onto a screen that is 0.350 m away from the grating. The first maxima contains all colors of light (ROYGBIV), but the color closest to the central fringe is violet and it is 7.00 mm from the central bright spot.

a. Calculate the wavelength of violet light

b. Red light has a wavelength of 700 nm…calculate the width of the fringe.

Speed Experiments

1. When Roemer discovered that light took an extra 22 minutes to reach earth and Huygens explained it to be a result of the light travelling the diameter of Earth's orbit they calculated the speed of light. Repeat the calculation - what value do you get for the speed of light?

2. At what frequency must Michelson spin a 10 sided mirror to observe his light source if the fixed mirror is 25.3 km away?

3a. A 12 sided mirror rotates at 871 Hz to produce an image in a Michelson

experiment. The fixed mirror is 14.3 km distant. What speed of light is calculated using these values?

b. The same 12 sided mirror will produce an image when it rotates at a frequency greater than 871, what is that frequency?

4. Michelson measured the speed of light by shining a bright light source on an 8- sided rotating mirror. It reflected off a plane mirror 35.0 km distance and the image of the light was observed when the mirror rotated with a frequency of 528 Hz.

From this data Michelson would calculate the speed of light to be a x 10^b m/s Round and record a with 3 significant digits.

5. As of February 2008, Voyager 1 was the most distant man-made craft in the universe at a distance of 15.7 billion kilometers (105.3 Astronomical Units) from the Sun. How much time would it take for a transmission leaving earth to reach Voyager I at the speed of light?

6. When you are having a conversation on a land line the sound is carried as light pulses in fibre optic cables. If the fibre optic has an index of refraction of 1.40 and the person you are talking to is 12.0 km away as the pulse travels, how long will it take for you to hear them say “No, I don’t want to talk to you, stop calling me or I’ll tell my mom.” Assuming, of course, that they say this.

Maxwell’s Illuminating Insight

The Electromagnetic Spectrum

1. Maxwell’s theory proposed that light was a form of EMR and that all EMR…

a. Was created by:

b. Was composed of:

c. Travelled at the speed of _____________ in a vacuum.

d. Had a frequency of oscillation that depended upon:

2. Radio waves are used in radar, visible light can detect objects the size of a bacteria.

What is the relationship between the EMR type and the object size?

3. Complete the chart.

EMR form Wavelength Frequency (Hz) speed (m/s) 2.00 m

infrared 900 nm

6.00 x 10¹⁴

X-ray 2.00 x 10¹⁷

4. Heinrich Hertz was the first to discover invisible EMR – he generated radio waves and used a simple detector – a loop of metal with a tiny spark gap. Explain how the radio wave could produce a spark.

5. Label one of these a microwave, the other an ultraviolet wave. Draw a wave of yellow light with the right measure reasonably represented. (I love alliteration)

6. Name the EM wave that:

a. has a wavelength of 1.0 cm b. reflects off the ionosphere

c. contains the peak of solar radiation d. is used in night-vision goggles e. can expose photographic paper f. is produced by unstable atomic nuclei g. is produced by suddenly stopping electrons h. can diffract around buildings

i. has wavelengths just a little too small for our eyes to see

j. will diffract around atoms and allow us to determine crystal spacing k. penetrates skin, but not bone

l. can scatter the atoms in bacterial DNA, so is useful in sterilizing hospital equipment m. carries tv signals

n. provides a nice tan, and causes skin cancer

o. can cause the hydrogen nuclei in your body to change their rotation.

p. can penetrate concrete

7. When you watch reporters answer questions from ½ a world away there appears to be a time lag from when the question is asked to when they hear it. What should that time lag be if the radius of the earth is 6.37 x 10⁶ m and the signal travels from one side of the planet, to a geosynchronous satellite 3.6 x 10⁷ m above the equator, and then back down to the reporter?

8. When you are having a conversation on a land line the sound is carried as light pulses in fibre optic cables. Isn’t that ironic. If the fibre optic has an index of refraction of 1.4 and the person you are talking to is 12 km away as the pulse travels, how long will it take for you to hear them say “No, I don’t want to talk to you, stop calling me or I’ll tell my mom.” Assuming, of course, that they say this.

Planck’s first Plank

1. Summarize: what is blackbody radiation?

2. Max Planck made sense of blackbody radiation, but it required a curious description for EMR – what was that description?

3. Explain the significance of this graph.

4. Complete the chart

EMR form Wavelength Frequency (Hz) Energy of a Quantum (J)

radio 2.00 m

infrared 900 nm

visible 6.00 x 10¹⁴

X-ray 1.33 x 10^-16

5. Rank these visible lights from most energetic to least: yellow, blue, red, green

6. Photosynthesis occurs by absorbing light energy and storing it in high energy chemical bonds. The alga Cladophora have been shown to use 656 nm and 486 nm light most effectively.

a. what color are these light?

b. what is the highest energy light used by Cladophora?

7. Hecht, Shlaer, and Pirenne published Visual Perception in 1942. Their experiment showed that about 90 photons at 510 nm must enter the eye aimed at the most sensitive spot for a person to see light. How much energy does this represent?

8. Hertz reflected his waves off of a curved mirror and determined their wavelength to be 66 cm. What type of waves was Hertz using in his experiment and what was the energy of one quantum of this em wave?

9. Wilhelm Roentgen was the first winner of the Nobel Prize, for his discovery of X-Rays, (also known as Roentgen Rays). At right is the first X-Ray – the hand of Mr. Roentgen’s wife. What is the energy of an X-Ray with a wavelength of 0.10 nm?

Einstein’s Explanation

We have seen the photoelectric effect is explained with Einstein’s leap of logic that light must have some particle-like nature. That is, EMR comes in little bundles that we call

“quanta” (singular: “quantum”), or photons.

Make an Energy vs. Frequency graph for 3 different materials and then interpret the results by answering the questions that follow.

 choose your scale your graph will show the y-intercept

 do not include the 0 photoelectron energy values.

Energy of Photoelectrons vs. Frequency of Incident Radiation

Wavelength (nm)

Frequency (Hz)

Photoelectron Energy (eV)

Sodium Silver Cesium

500 0 0 0.4

450 0 0 0.5

400 0.4 0 1.0

350 0.7 0 1.5

300 1.4 0 2.0

250 2.2 0.7 2.9

Kinetic Energy of

photo- electrons

(eV)

Frequency of incident radiation (x10¹⁴ Hz)

Analysis Questions

1. Calculate and compare the slope of the sodium and cesium lines.

2. The value of the slope of each line is a fundamental physical constant a. what is the name of this constant

b. convert the value you have calculated in eV/Hz into J·s and calculate a percent difference with the value provided on your data table.

3. Based on your answer to #1 you should be able to draw the silver line despite having only one point. Draw it on your graph.

4. From your graph determine the threshold frequency for each metal.

5. Determine the work function of each of the metals a. using the x-intercept

b. using the y-intercept

6. A silver surface is illuminated by emr with a wavelength of 10.0 nm a. Does this light have sufficient energy to eject an electron?

b. A current of 2.0 μA is measured what minimum number of photons hit the surface every 1.0 s?

c. What is the maximum kinetic energy of the ejected electrons?

d. What stopping potential would be required?

7. Use your knowledge of the periodic table to make a hypothesis as to why silver has a larger threshold frequency than either cesium or sodium.

8. Explain the photoelectric effect in terms of energy conservation.

9. Explain why not all photoelectrons ejected from a surface will have the same energy.

X-Rays and X-Ray Production

As with any vacuum tube, there is a cathode, which emits electrons into the vacuum and an anode to collect the electrons, thus establishing a flow of electrical current, known as the beam, through the tube. A high voltage power source, for example 30 to

150 kilovolts (kV), is connected across cathode and anode to accelerate the electrons.

The X-ray spectrum depends on the anode material and the accelerating voltage. The X- ray photon-generating effect is generally called the Bremsstrahlung effect, a contraction of the German bremsen for braking, and strahlung for radiation. Wikipedia.

1. Analyze the diagram above to explain the following:

a. How are electrons accelerated to high speeds?

b. Why must the X-ray tube be evacuated (have no air)?

c. What principle relates the voltage the electrons pass through to the wavelength of the produced X-Rays?

d. Show algebraically the relationship between the wavelength of the X-ray and the voltage the electrons passed through.

e. In an experiment a research manipulated the accelerating voltage and measured the resulting wavelength of the X-rays produced. A graph of photon wavelength vs. __________ would produce a straight line with a slope of ___________.

2. An X-ray tube is operating and produces photons with a wavelength of 100 pm.

a. The energy of these photons is _______ x 10 ^–wz J b. The accelerating potential difference is _____ x 10^w V.

3. Calculate the wavelength of a 150.00 keV photon.

4. The frequency of a soft X-ray photon used in medical diagnosis is 3.2 x 10¹⁶ Hz. It has a wavelength of a.b x 10^-c m

5. The momentum of a 50 pm X-ray photon is a.b x 10^-cd kgm/s.

Compton’s Essential Duality

1. The Compton Effect (identified in 1923) describes the result of a high energy X-ray photon colliding with an electron in orbit around ant atom. What concept did Compton use to explain the results of this collision?

2a. Calculate the momentum of a photon of red light with a wavelength of 650 nm.

b. How many such photons would be required to have the same momentum as an electron which has passed through a potential difference of 12 V?

3. Find the momentum of a 50 pm photon.

4. An iron atom at rest emits a 6.4 keV X-ray photon, calculate the recoil momentum of the atom.

5. If a 10 pm X-Ray is scattered by collision with an electron and becomes an 11 pm X- ray, what is the angle between the incident and the scattered X-rays?

6. A 50.0 pm wavelength X-Ray collides with an electron and causes the Compton Effect. The scattered photon leaves at 70° from the original direction of travel.

a. What is the wavelength of the scattered photon?

b. How much energy does the electron gain?

7. Use vector addition principles to determine the direction of travel of the scattered electron given this diagram - which represent the momentum of the incoming and scattered X-rays. (Note: tip-to-tail diagram required!)

8. Use vector addition principles to determine the momentum and wavelength of a scattered photon based on this information:

Incoming X-ray wavelength: 50 pm

Scattered electron momentum: 2.2 x 10^-24kgm/s, 60° from the direction of the incoming X-ray.

high energy X-ray collides with an atom.

e^-

lower energy X-ray and an electron are ejected.

Answers

Straight Lines… p2

1. sharp shadows, pinhole camera 2. dark

3.

4. Newton, Huygens Law of Reflection

5. angle between incoming ray and a line perpendicular to the surface 6. 80°

7. 50°

8. 1.10 m 9. 27.5°

Curves and Rays

1.

2.

vertex focus

centre axis

Curved Mirrors, p 4

4. a. image starts at focus and moves to centre b. starts at centre and moves out toward infinity

c. starts at infinity and immediately flips to virtual image behind mirror d. starts at focus and moves to mirror (see diagram g above).

Law of Refraction …p5 1. particle theory – it speeds up wave theory – it slows down 2a.

b. incoming and outgoing rays are parallel c. high

3. 10.2°

4. n = 1.55 5. 61.9°

6a 48.8° (water) b. 63.2° (sugar) 7a. 3.00 x 10⁸ m/s – air b. 2.26 x 10⁸ m/s – water c. 2.29 x 10⁸ m/s – ice d. 1.24 x 10⁸ m/s – diamond

8. light reaches boundary at an angle greater than the critical angle at the bottom of the diamond.

Max’s Insight page 9

1. a. accelerating charges b. changing fields c. 3.00 x 10⁸ m/s d. f of source

2. The wavelength corresponds to the smallest object that can be detected.

3.

4. changing magnetic field causes generator effect 5. yellow is between the short wave length UV and long wavelength microwave, amplitude does not matter.

6. a. micro; b. radio; c. visible; d. infrared; e. visible or higher frequency; f. gamma; g. X-ray; h. radio; i. UV;

j. X-ray; k. X-ray (soft); l. UV; m. radio; n. UV o.

radio; p. gamma 7. 0.29 s 8. 5.6 x 10^-5 s Planck’s first Plank Page 11

1. EMR emitted from a perfect absorber. Theoretically such an object should be able to emit all forms of EMR.

2. EMR is quantized… i.e. it has a particle nature.

3. Classical theory can’t explain blackbody radiation – we must think of light as quantized.

4.

5. blue, green, yellow, red

6. a. 656 nm – red; 486 – blue/green b. b-g light E = 4.09 x 10^-19 J or 2.56 eV 7. 219 eV

8. radio; 1.88 x 10^-6 eV 9. 12.4 MeV

Xrays and Xray Production 1a. with an electric field

b. air molecules would deflect them c. conservation of energy

d. λ = hc/qV

e. 1/V and slope = 1.24 x 10^-6 2a. 1.99 x 10^-15 J

b. 1.24 x 10⁴ V 3. 8.28 x 10^-12 m

4. 9.38 x 10^-9 m (9.4 with 2 sig digs) 5. 1.33 x 10^-23 (record 1.3)

Compton’s Essential Duality page 14

1. momentum is conserved.

2a. 1.02 x 10^-27 kg b. 1.8 x 10³ 3. 1.3 x 10^-23 kgm/s 4 3.4 x 10^-24 kgm/s 5. 54.0°

6a. 51.6 pm b. 1.3 x 10^-16 J 7.

8. a. 1.23 x 10^-23 kgm/s at 8.9°

b. 53.9 pm Radio 2.00 m 1.50 x 10⁸ 3.00 x 10⁸

Infrared 900 nm 3.33 x 10¹⁴ 3.00 x 10⁸ Visible 500 nm 6.00 x 10¹⁴ 3.00 x 10⁸ X-ray 1.50 nm 2.00 x 10¹⁷ 3.00 x 10⁸

Radio 2.00 m 1.50 x 10⁸ 9.9 x 10^-26 Infrared 900 nm 3.33 x 10¹⁴ 2.19 x 10^-19 Visible 500 nm 6.00 x 10¹⁴ 3.98 x 10^-19 X-ray 0.62 nm 4.83 x 10¹⁸ 1.33 x 10^-16