Astigmatism: cornea curvature not spherical, different focal lengths in different planes. Corrected by cylindrical lens which has different powers in perpendicular axes. Not simple spherical lens.
Explanation:
B ∝ N. Double turns ⇒ double field at center. Direct proportionality from Biot-Savart law. Memory tip: 'Coil field: B ∝ NI; more turns ⇒ stronger field'. Magnetism formula frequently tested in competitive exams.
Explanation:
Free fall: h = ½gt² ⇒ t = √(2h/g). Thus t ∝ √h. If h' = 4h, t' = √(4h/g) = 2√(h/g) = 2t. Time doubles when height quadruples. Memory aid: 'Free fall time: t ∝ √h; quadruple height ⇒ double time'. This kinematics proportional reasoning problem is frequently tested in competitive exams. Always derive the proportionality from fundamental equations; avoid assuming linear relationships for non-linear motion.
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