The focal length of a spherical mirror is related to its radius of curvature R by:
A. f = R
B. f = 2R
C. f = R²
D. f = R/2
Answer: Option D
Solution (By JKSSB Mock Tests)
For spherical mirrors (concave or convex), focal length f = R/2, where R is radius of curvature. This holds under paraxial approximation (small angles). Derivation uses geometry of reflection and small-angle approximations. Memory tip: 'Mirror: f = R/2; Lens: 1/f = (n-1)(1/R₁ - 1/R₂)'. This fundamental relation is frequently tested in optics sections of competitive exams. Always note sign conventions: f negative for convex mirrors, positive for concave; R follows same sign as f.
Explanation:
Refractive index n = c/v, where c = 3×10⁸ m/s (speed in vacuum). Thus v = c/n = (3×10⁸)/(4/3) = 3×10⁸ × 3/4 = 9/4 × 10⁸ = 2.25×10⁸ m/s. This direct formula application is fundamental in optics. Memory aid: 'Higher n ⇒ slower light in medium'. Competitive exams frequently test this calculation with common refractive indices (water 4/3, glass ~1.5). Always use c = 3×10⁸ m/s unless specified otherwise, and ensure unit consistency (m/s here).
Explanation:
Joule's Law of Heating states that the heat (H) produced in a resistor is given by H = I²Rt. This indicates that the heat produced is directly proportional to the square of the electric current (I), directly proportional to the resistance (R), and directly proportional to the time (t) the current flows.
Explanation:
The gravitational potential V inside a uniform solid sphere at a distance r from the center is V = -GM * (3R^2 - r^2) / (2R^3). At the exact center of the Earth, r = 0. Substituting r = 0 gives V = -GM(3R^2) / 2R^3 = -3GM / 2R. The potential is strictly non-zero and highly negative.
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