Explanation:
Diamonds are cut in such a way that light entering them hits multiple facets from the inside at an angle greater than the critical angle (which is very low for diamond, around 24.4°). This results in multiple total internal reflections, trapping light and forcing it out of specific faces, creating a brilliant sparkle.
Explanation:
Photoelectric equation: work function φ = hν₀, where ν₀ is threshold frequency. Thus ν₀ = φ/h = 2.3 eV / (4.14×10⁻¹⁵ eV·s) ≈ 5.555×10¹⁴ Hz ≈ 5.6×10¹⁴ Hz. This direct application tests photoelectric effect fundamentals. Memory aid: 'ν₀ = φ/h; higher work function ⇒ higher threshold frequency'. Competitive exams frequently provide h in eV·s for such calculations. Always ensure units match: eV for φ and h to avoid conversion errors. This problem assesses numerical proficiency in modern physics applications.
Explanation:
Range R = u²sin(2θ)/g. sin(2θ) maximum (=1) when 2θ=90° ⇒ θ=45°. Standard result for level ground projection. Memory aid: 'Max range at 45°; max height at 90°'. Projectile motion fact frequently tested in competitive exams.
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