Powerpoint on how to prove the Speed of Light with Chocolate and Marshmallows :)

1. S’mores
at the Speed of Light
How we accurately and deliciously measured the universal
constant velocity of electromagnetic radiation

2. Electromagnetic Waves
• When an Electric Field is Generated, a Magnetic Field is generated
• When an Electric Field changes it’s Magnetic Field is also changes
• These changes propagate outward through at a constant speed
• These radiating propagations are Electro-Magnetic Waves, or Electromagnetic
Radiation
• Because we are most familiar with the visible spectrum of electromagnetic
radiation, we call their velocity the Speed of Light.
Skip to Experiment

3. WARNING
The Following Section contains:
EXPLICIT MATHEMATICS
and a LOT OF ALGEBRA

4. Maxwell’s Equations
• 𝟇 𝐵 = 𝐵 ∙ 𝑑𝓁 = 𝐵𝓁
• 𝟇 𝐸 = 𝐸 ∙ 𝐴 = 𝐸𝐴
• 𝐸 ∙ 𝑑𝓁 =
−𝑑𝟇 𝐵
𝑑𝑡
• 𝐵 ∙ 𝑑𝓁 = 𝜇0 𝜖0
𝑑𝟇 𝐸
𝑑𝑡
• distance covered by wave in a
period of time ∆𝑡: 𝑐0∆𝑡
• 𝐴 = 𝐸𝓁𝑐0∆𝑡
• ∆𝟇 𝐸= 𝐸𝓁𝑐0∆𝑡 − 0
• Rate of Change in Electric Flux:
∆𝟇 𝐸
∆𝑡
= 𝐸𝓁𝑐0

5. Rate of Change of
Electric Flux
• Rate of Change in Electric Flux:
∆𝟇 𝐸
∆𝑡
= 𝐸𝓁𝑐0
• Combine with: 𝐵 ∙ 𝑑𝓁 = 𝜇0 𝜖0
𝑑𝟇 𝐸
𝑑𝑡
• yields: 𝐵𝓁 = 𝜇0 𝜖0 𝐸𝓁𝑐0
• Simplified: 𝐵 = 𝜇0 𝜖0 𝐸𝑐0

6. Rate of Change of
Magnetic Flux
• Rate of Change in Magnetic Flux:
𝐸 ∙ 𝑑𝓁 =
−𝑑𝟇 𝐵
𝑑𝑡
• On a rectangular path
𝐸 ∙ 𝑑𝓁 = 𝐸𝑤
• If a magnetic field traces the same
path,
−𝑑𝟇 𝐵
𝑑𝑡
= −𝐵𝑤𝑐 𝑜

7. ALMOST THERE!!!

8. More Algebra…
•E𝑤 = 𝐵𝑤𝑐 𝑜
•
𝐸
𝑐 𝑜
= 𝐵𝑤
•
𝐸
𝑐 𝑜
= 𝜇0 𝜖0 𝐸𝑐0

9. Finally…
The Velocity of
Electromagnetic Radiation:
𝑐 𝑜 =
1
𝜇0 𝜖0

10. Finally…
The Velocity of Electromagnetic
Radiation:
𝑐 𝑜 =
1
𝜇0 𝜖0
• In a vacuum,
𝜖0 = 8.854𝑥10−12
𝜇0 = 4𝜋 𝑥10−7
𝑐 𝑜 = 299,792,458 𝑚/𝑠

11. How do we PROVE this?!
(This is the part that tastes good!)

12. Wave Function
The essential function of a wave is:
𝜆 =
𝑣
𝑓
Given the frequency 𝑓 of a wave, we can obtain the velocity 𝑣 by the equation
𝑣 = 𝜆𝑓
where 𝜆 is the wavelength.

13. Electromagnetic Wave
Exposure Chamber
(of science!)
1250 Watt Cooking Power
2450 MHz Operating Frequency
Modified to prevent any plate rotation

14. Constructive Wave
Interference
Waves from a common source (the
Microwave-oven magnetron in this case) will
share a common wavelength, frequency, and
path of travel..
These waves will interfere with one another
as they propagate outward.
The regions that receive the highest amplitude of
energy will develop “hot spots”, while the “nodes”
receive significantly less heat.

15. Measure the “Hotspots”
• If we measure the distance between the hotspots, we will find points of
highest amplitude along the wave.
• Since the energy transferred to a substance is irrespective of sign, both the
“peak” and “trough” of a wave will generate these hotspots
• Therefore, the distance between hotspots is
𝜆
2
• and 𝑣 = 2𝑑𝑓

16. Experiment 1:
Distributed Thermal
Reception Modules
•Provides a measurable surface
•Visible Physical Change on Reception
of Microwave

17. Experiment 1:
Distributed Thermal
Reception Modules
Densely packed
approximately 1cm units

18. Cook for ~30 seconds

19. Measure
Hotspots
•Bands of marshmallows melt together
•Others remain cold or are pulled apart.
•Measurement:
~6cm

20. 2nd-run of Experiment 1
Approximately ~6cm

21. Experiment 2:
Contiguous Thermal
Reception Substrate
•Provides a solid surface
•Low Melting Point
•If exposed for short time,
will partially melt

22. Experiment 2:
Contiguous Thermal
Reception Substrate
Using distributed method a tool to
determine optimal alignment within
the oven
Cook for ~45 seconds

23. Enhancements for
Precise Measurement
While still warm, drag a knife across the
chocolate.
Hot spots will show clearly in the mark
made by the knife
Bisect these lines to determine the center of
each peak

24. Precision Measurement
Determined distance between hotspots as
6.0cm
or
d = 6.0x10−2 𝑚

25. Analysis and Conclusion
• Our most precise measurement: d = 6.0𝑐𝑚
• Our formula derived from the Wave function: 𝑣 = 2𝑑𝑓
• 𝑣 = 2(6.0𝑐𝑚) 2450𝑀𝐻𝑧 = 294,000,000𝑚/𝑠
• How does this compare to the accepted value of 𝑐 𝑜 = 299,792,458 𝑚/𝑠
• Difference: 2%
𝑐 𝑜 𝐡𝐚𝐬 𝐛𝐞𝐞𝐧 𝐞𝐱𝐩𝐞𝐫𝐢𝐦𝐞𝐧𝐭𝐚𝐥𝐥𝐲 𝐜𝐨𝐧𝐟𝐢𝐫𝐦𝐞𝐝‼!

26. Special Thanks
to our Junior Lab Assistants for assisting
with the science.