Rotating-analyser graph
cos² shape: maxima at 0°, 180°, 360°, zeros at 90°, 270°, period 180°, never negative. Unpolarised source through a polariser THEN a rotating analyser: maxima at ½I₀. A single polaroid rotating in unpolarised light gives constant ½I₀ — no zeros (that constancy IS the unpolarised verdict). Applications: polaroid sunglasses (cut horizontally-polarised glare), 3-D cinema (orthogonal filters per eye).
What this actually means
Transmitted intensity against analyser angle is a cos² curve: maxima at 0°, 180° and 360°, zeros at 90° and 270°, period 180°, and never negative.
Feed unpolarised light through a fixed polariser first and the maxima of that curve sit at ½I₀, because the half was taken upfront.
A single polaroid rotating in unpolarised light draws a flat line at ½I₀ instead. Real uses to quote: polaroid sunglasses cut horizontally polarised glare; 3-D cinema sends each eye orthogonally polarised images.
Prove it — watch it be true
- Sweep the analyser through 360° and watch the cos² curve draw itself
- Count the features: two maxima, two zeros, period 180°
- Note the maxima sit at half the source intensity — the upfront ½ again