Lecture 8: The single slit
Learning Goals
- Develop Feynman’s model for how light travels from one point to another employing the rules of quantum mechanics.
- prerequisite: You should be familiar with the quantum model for how light partially reflects from the surface of glass.
- After this lesson, you will be able to:
- Describe how light appears to travel in straight lines.
- Explain what happens when light is forced to travel through a narrow slit.
- Understand how slit width depends on the color of the light.
- Stretch goal: You may be able to explain the single-slit diffraction patterns that develop when light travels through a narrow slit.
Introduction: Why Single and Multiple Slits?
Having mastered partial reflection and the concept of a photon undergoing quantum interference, we now move to a different series of experiments — ones that will ultimately unveil the quantum mystery.
The experiment is simple:
Shine light at a dark screen that has one or more slits cut into it, and look at the pattern of light that hits a second screen far away.
Despite its apparent simplicity, this experiment holds the key to understanding both quantum mechanics and the behavior of light.
Light traveling through a single slit can be thought of as a test of the question: Does light travel in a straight line? — and why.
Feynman’s Quantum Model for Light Travel
Key Insight
In the quantum theory, many paths contribute to the light that goes through a narrow slit — not just the path with the shortest length (the straight-line path).
- For paths near the shortest-distance path, the length changes slowly, so the arrows (probability amplitudes) do not turn significantly more. These paths contribute strongly to the final arrow.
- When there is no straight-line path, the times for different paths increase more rapidly, so the arrows for different alternatives tend to spin around, and their sum goes nowhere — resulting in a small final arrow.
If these facts are not clear, revisit the computer tutorial and pay close attention to these two ideas.
The Role of Color (wavelength)
The color of light determines how fast the stopwatch hand rotates:
| Color | Relative Rotation Rate | Relative Wavelength | Relative Energy |
|---|---|---|---|
| Red | Slowest (~36,000 rotations/inch) | Longest (~1/36,000 inch ≈ 0.7 μm) | Lowest |
| Green | ~50% faster than red | ~50% less than red | Medium |
| Blue | ~2× faster than red | ~2× less than red | Highest |
Key Relationships
- Photon energy is proportional to rotation rate — blue light carries more energy than green, which carries more than red.
- Wavelength is defined as the distance the photon travels during one full revolution of the clock.
Practical Consequences
- Ultraviolet light (even faster rotation / higher energy) is used to initiate chemical processes.
- UV light causes sunburns; infrared light (slower rotation / lower energy) makes sunlight feel hot on your skin.
(Video demonstration — “Squeezing Photons Through a Narrow Slit,” MIT Physics Department)
Changing the Slit Width
- A red laser is used in the demonstration, and the slit width is varied.
- When the slit is wide → light travels in nearly straight lines (predictable, particle-like).
- When the slit is narrow → light spreads out dramatically (wave-like diffraction).
The pattern seen when the slit is made extremely narrow is relevant to the famous debate in the movie Big Bang.
Changing the color of light acts similarly to changing the width of the slit opening — increasing frequency (red → blue) is comparable to narrowing the slit.
Open Exploration Questions
After working through the compute engine tutorials, consider these questions:
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Straight lines vs. spreading: How can light tend to travel in straight lines, yet spread out when squeezed through a narrow slit? Does this relate to Heisenberg’s uncertainty principle?
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Color-slit equivalence: Explore how increasing the frequency of light (red → blue) compares with narrowing the slit.
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Diffraction fringes: The video shows interesting diffraction patterns at the outer edges. Use the compute engine to see if you can find an arrangement that describes this behavior.
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Slit width as a microscope: Since narrowing the slit expands the pattern, could you measure slit width from the pattern size if you know the wavelength? In this sense, the single-slit experiment is like a microscope.
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What’s next? What will happen when we add a second slit?
Key Takeaways
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Many paths contribute: In quantum mechanics, light does not simply follow the shortest path. All paths contribute, but those near the straight-line path contribute the most because their arrows point in similar directions.
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Color = rotation rate = energy: The color of light directly encodes the photon’s energy and wavelength. Blue light has higher energy and shorter wavelength than red light.
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Slit width controls diffraction: Narrowing the slit causes light to spread out more — a direct manifestation of quantum interference among the available paths.
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Color and slit width are linked: Changing the color of light has a similar effect to changing the slit width. This connection is fundamental to understanding diffraction.
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The single slit is just the beginning: This setup prepares us for the two-slit experiment, which contains the central mystery of quantum mechanics.
Historical note: Joseph von Fraunhofer (1787–1826) is generally credited with first solving the problem of diffraction from a single slit.