Govt. Exams
Entrance Exams
For constructive interference, phase difference = 0, 2π, etc. For destructive interference, phase difference = π, 3π, etc. Phase difference of π/2 gives partial or incomplete interference with intermediate intensity.
Using lens maker's formula: 1/f = (n-1)[1/R₁ - 1/R₂]. For plano-convex: 1/f = (1.5-1)[1/R - 1/∞] = 0.5/R. Therefore f = 2R.
For single-slit diffraction, minima occur at positions where a·sin(θ) = mλ, where m = 1, 2, 3... Since sin is approximately proportional to θ for small angles, the second minimum occurs at approximately 2θ.
For a concave mirror, when object is between F and C, the image is real, inverted, and magnified. This is the magnification region used in shaving mirrors.
Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂). So 1.5 × sin(30°) = 1.0 × sin(θ₂). This gives sin(θ₂) = 0.75, therefore θ₂ = 48.6°
Power P = 1/f. f = 1/5 = 0.2 m = 20 cm. Positive power indicates convex lens.
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.
