Govt. Exams
Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂). So 1.33 × sin(30°) = 1.5 × sin(θ₂). Therefore 1.33 × 0.5 = 1.5 × sin(θ₂), which gives sin(θ₂) = 0.443, θ₂ ≈ 27.8°.
Fringe width β = λD/d = (500 × 10⁻⁹ × 1)/(0.5 × 10⁻³) = 500 × 10⁻⁶/0.5 × 10⁻³ = 1.0 mm.
Using lens formula: 1/f = 1/v + 1/u. For concave lens, f = -20 cm, v = -10 cm (virtual image). So 1/-20 = 1/-10 + 1/u gives 1/u = -1/20 + 1/10 = 1/20, therefore u = 20 cm.
When a plane mirror moves towards an object with velocity v, the image also moves towards the mirror with velocity v. The relative velocity of approach between object and image is 2v. Therefore, velocity of image = 2 × 2 = 4 m/s.
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.
