Govt. Exams
In a plane mirror, image distance equals object distance. Total separation = u + v = 50 + 50 = 100 cm
sin(θc) = n₂/n₁ = 1/1.5 = 2/3. θc = arcsin(0.667) = 41.81°
Using lens formula: 1/f = 1/u + 1/v. 1/15 = 1/30 + 1/v. 1/v = 1/15 - 1/30 = 1/30. v = 30 cm (real image)
Diffraction and interference are characteristic wave phenomena. Other options demonstrate particle nature of light.
Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂). 1×sin(30°) = 1.5×sin(θ₂). sin(θ₂) = 0.5/1.5 = 1/3. θ₂ = 19.47°
For circular motion in a magnetic field: qvB = mv²/r, which gives r = mv/(qB). Therefore, momentum p = mv = qBr = eBr (for an electron where q = e).
Magnetic moment M = IA, where I is the current and A is the area enclosed by the loop. For N turns, M = NIA. The SI unit is A·m².
The magnetic field inside an ideal long solenoid is B = μ₀nI, independent of the solenoid's radius and position along the axis (away from ends). This assumes n is the number of turns per unit length.
When a charged particle moves perpendicular to a uniform magnetic field, the Lorentz force acts as centripetal force, causing circular motion. The radius is r = mv/(qB).
Parallel wires carrying currents in the same direction experience attractive force. Force per unit length = μ₀I₁I₂/(2πd). If currents are opposite, the force is repulsive.
