Govt. Exams
When mirror moves towards object at speed v, the image also moves towards object at speed v. Therefore, relative speed = v + v = 2v = 10 m/s
n = c/v. 1.5 = (3 × 10⁸)/v. v = (3 × 10⁸)/1.5 = 2 × 10⁸ m/s
Power combination: P = P₁ + P₂ = 5 + (-2) = 3 D. Focal length f = 1/P = 1/3 = 0.33 m
Using mirror formula: 1/f = 1/u + 1/v. 1/10 = 1/15 + 1/v. v = 30 cm. Magnification m = -v/u = -30/15 = -2
For total internal reflection from denser to rarer medium, sin(θc) = n₂/n₁ where n₁ is refractive index of denser medium and n₂ of rarer medium
Fringe width β = λD/d. If d is doubled, β becomes β/2, i.e., half of the original value
Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂). 1.5 × sin(30°) = 1.0 × sin(θ₂). 1.5 × 0.5 = sin(θ₂). sin(θ₂) = 0.75, θ₂ = 48.6°
Frequency f = c/λ = (3 × 10⁸)/(632.8 × 10⁻⁹) = (3 × 10⁸)/(6.328 × 10⁻⁷) ≈ 4.74 × 10¹⁴ Hz.
Grating constant d = 1/(number of lines per unit length) = 1/5000 cm⁻¹ = 2.0 × 10⁻⁴ cm or 2 μm.
At critical angle: sin(θc) = 1/n. So sin(45°) = 1/n gives 1/√2 = 1/n, therefore n = √2 ≈ 1.41.
