Diffraction & Polarization
The narrower the gap, the wider the spread. And a third polariser lets light through two that had blocked it completely.
Introduction
Look at a bright line of light through the gap between two fingers. As the gap closes, the light smears out into stripes, and the smaller the gap, the wider the smear.
Light of one colour passes through a single slit onto a distant screen. You halve the slit's width. What happens to the bright central patch?
One slit
The dark bands are where the light from one half of the slit arrives out of step with the light from the other half. Write that down carefully and the condition falls out.
For the single slit the condition is a sin θ = mλ with m = ±1, ±2, … Why is m = 0 left out?
Many slits
Now cut many parallel slits instead of one. Common sense says: more slits, more light, brighter fringes in the same places. Half of that is right.
You replace a double slit with a grating of the same spacing d but 500 rulings, using the same light. What happens to the first-order line?
What the light is waving
Everything so far would work as well for sound. The next experiment does not.
Two polarisers are crossed at 90°, and no light gets through. You slide a third polariser, at 45°, into the gap between them. What comes out the far side?
A third polariser
A polariser is not a sieve that removes the light pointing the wrong way. It projects: whatever arrives leaves oscillating along its axis, with the amplitude reduced by and the intensity by . The short marks along each beam show it: after each polariser they all point along its axis.
What comes next
Two threads run out of this lesson. Gratings turn light into a measurement: every wavelength quoted for a distant star was read off an angle. And squeezing a wave through a narrow gap makes its direction less certain, the more so the narrower the gap: a sentence about waves here, and later a sentence about particles.
Ideas this lesson took on
Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.
- “A narrower slit makes a narrower beam”
- “More slits push the bright lines further out”
- “The single-slit and grating formulas are the same rule with different letters”
- “A polariser can only ever take light away”
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Research behind this lesson
- Ambrose et al. 1999: University students who had studied physical optics at introductory level and beyond often could not account for the pattern light makes on a screen after a single or double slit; many did not know whether to apply geometrical or physical optics to a given situation and inappropriately combined elements of both, and some difficulties were serious enough to preclude even a qualitative wave model for light.
- Matejak Cvenic et al. 2021: Twenty-seven Croatian students aged 18–19, interviewed after regular instruction on polarization of light, showed conceptual difficulties that survived teaching; they often based their explanations on remembered but misinterpreted common schematic representations of polarization rather than on any model of light.
- Maurines 2010: Two hundred French students aged 19–23, questioned after lessons on wave optics, repeatedly reverted to geometrical reasoning: they followed the rays of the incident light at a macroscopic level instead of reasoning at the level of elementary waves with the phase concept and the Huygens–Fresnel principle.
- Wosilait et al. 1999: Evidence that university students frequently lack a functional understanding of the wave model for light, together with the design of research-based tutorials intended to build that model rather than supply more formulas.