The angle of minimum deviation for a prism depends on:
A. Both angle of prism and refractive index
B. Wavelength of light only
C. Refractive index only
D. Angle of prism only
Answer: Option A
Solution (By JKSSB Mock Tests)
Minimum deviation δ_m for a prism: n = sin[(A + δ_m)/2] / sin(A/2), where A is prism angle, n refractive index. Thus δ_m depends on both A and n. Since n varies with wavelength (dispersion), δ_m also depends on wavelength, but the primary dependencies are A and n. Memory tip: 'δ_m increases with A and n; used to measure n'. This optics formula application is frequently tested in competitive exams. Always recall that minimum deviation occurs when ray passes symmetrically through prism, a key condition for derivation.
Explanation:
The loudness level in decibels is calculated as L = 10 * log10(I / I0). If intensity I becomes 100I, the new level L' = 10 * log10(100I / I0) = 10 * [log10(100) + log10(I / I0)] = 10 * [2 + L/10] = 20 + L. Therefore, the loudness explicitly increases by 20 dB.
A particle performs Simple Harmonic Motion (SHM). If its displacement from the mean position is half of its amplitude, the ratio of its kinetic energy to potential energy is:
Explanation:
In SHM, Total Energy (E) = 1/2 k A^2. Potential Energy (U) at displacement x is 1/2 k x^2. Kinetic Energy (K) is E - U = 1/2 k (A^2 - x^2). Given x = A/2. U = 1/2 k (A/2)^2 = 1/2 k (A^2 / 4) = E/4. Since total energy is conserved, K = E - E/4 = 3E/4. The ratio of Kinetic to Potential Energy (K:U) is (3E/4) / (E/4) = 3:1.
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