PTC Practice Problem – Refraction and Snell’s Law
Question:
A ray of light traveling through air is incident on a flat vertical mirror. The ray arrives at the mirror with an angle of incidence of 65.00°. After reflecting from the mirror, the light enters carbon disulphide (refractive index n = 1.628). The mirror and the surface of the carbon disulphide are separated vertically by 10.00 cm, and the carbon disulphide layer is 32.00 cm thick.
- (a) Find the angle of refraction inside the carbon disulphide.
- (b) Determine how far from the corner the ray exits the carbon disulphide.
Answer and Explanation:
Step 1: Apply Snell’s Law to Find Angle of Refraction
We use Snell’s Law:
Where:
- n₁ = 1.00 (air)
- θ₁ = 65.00°
- n₂ = 1.628 (carbon disulphide)
sin(θ₂) = 0.6144 × 0.9063 ≈ 0.5567
⇒ θ₂ = sin⁻¹(0.5567) ≈ 33.78°
Step 2: Calculate Horizontal Exit Distance
We now use trigonometry to find the horizontal distance the ray travels while passing through the 32.00 cm thick carbon disulphide:
= 32.00 × 0.6702 ≈ 21.45 cm
Add the vertical separation (from mirror to CS₂ surface):
✅ Final Answers:
(a) Angle of refraction inside carbon disulphide: 33.78°
(b) Distance from the corner where the ray exits: 31.45 cm