Explanation:
Dispersion (splitting of white light into colors) occurs because refractive index n varies with wavelength (Cauchy's relation: n ∝ 1/λ² approximately). Since v = c/n, different colors travel at different speeds in the medium, causing different refraction angles (Snell's law). Frequency remains constant across media. Memory tip: 'Dispersion: n(λ) ⇒ v(λ) ⇒ different bending; violet bends most (highest n)'. This optics concept is frequently tested in competitive exams. Always distinguish cause (speed variation) from property (frequency/wavelength); competitive exams often test this nuanced understanding.
Explanation:
Average speed = Total distance / Total time. Let distance AB = d km. Time for AB = d/40 h, time for BA = d/60 h. Total distance = 2d km. Total time = d/40 + d/60 = d(3+2)/120 = 5d/120 = d/24 h. Average speed = 2d / (d/24) = 48 km/h. Note: Average speed is not arithmetic mean of speeds (which would be 50 km/h) because time intervals differ. This harmonic mean concept is crucial for motion problems. Exam tip: For equal distances, average speed = 2v₁v₂/(v₁+v₂). Frequently tested in competitive exams.
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