### Top 5 Long Derivations Every Student Must Memorize:
1. **Gauss's Theorem:** Electric field due to an infinite line charge and spherical shell.
2. **Lens Maker's Formula:** 1/f = (μ - 1)(1/R1 - 1/R2) with complete ray diagram.
3. **Biot-Savart Law:** Magnetic field at the axis of a circular current-carrying loop.
4. **Compound Microscope:** Magnifying power derivation for normal adjustment and least distance of distinct vision.
5. **Photoelectric Effect:** Einstein's photoelectric equation and threshold frequency verification.
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