Related Problems with Solution
Problem 1 : A beam of light travels from air into a glass slab (refractive index 1.5). If the angle of incidence is 45 degrees, calculate:
(a) The angle of refraction.
(b) The lateral shift of the beam when it enters the glass.
Solution :
(a) Using Snell’s Law: n₁sinθ₁ = n₂sinθ₂
- n₁ = refractive index of air = 1.0
- n₂ = refractive index of glass = 1.5
- θ₁ = angle of incidence = 45 degrees
Substituting these values, we get: 1.0 * sin(45°) = 1.5 * sin(θ₂) sin(θ₂) = (1.0 * sin(45°)) / 1.5 sin(θ₂) = 0.3333 θ₂ ≈ 19.47 degrees
(b) Lateral shift (d) can be calculated using the formula: d = t * tan(θᵣ - θᵢ), where t is the thickness of the glass slab.
- θᵣ = angle of refraction = 19.47 degrees
- θᵢ = angle of incidence = 45 degrees
- t = thickness of the glass slab (you need to be given this value)
