PHALIN THAKKAR
Notebook notes
Twelve explanations that follow a question through its mathematics, an example and a further challenge.
Why the square matters
Why does projection give cosθ while intensity gives cos²θ?
02 · Explanatory noteWhere the reference intensity belongs
What quantity is the denominator, and what uncertainty does it share with the numerator?
03 · Explanatory noteA good fit does not name the cause
What does a residual pattern suggest, and what additional check would test its cause?
04 · Explanatory noteMore measurements, same ambiguity
Which ambiguities can new settings remove, and which remain even with perfect readings?
05 · Explanatory noteWhy zero and 180 degrees agree
Why does changing the field sign preserve intensity, and how should angular errors be reported?
06 · Explanatory noteTwenty five percent, under which assumptions?
Which trials enter the denominator, and what does a finite sample show?
07 · Explanatory noteWhat the animation is actually showing
Which displayed values are computed, and what does the animation leave out?
08 · Explanatory noteTeaching the surprising part
Why can another filter increase the final output while every stage removes intensity?
09 · Research extensionFitting a direction without searching every angle
How does the double angle identity turn the fit into a linear algebra problem?
10 · Research extensionWhich analyzer settings carry more information?
Is the brightest reading always the most informative about an unknown angle?
11 · Research extensionWhat linear analyzer readings leave out
Can intensity readings recover a complete polarisation state?
12 · Research extensionMore intermediate filters, more transmission?
What changes if several ideal projections share the rotation between crossed axes?
The research extensions go beyond school and JEE material. They are not presented as examination syllabus content.