A narrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air through a 1.80 cm thick flat piece of crown glass and back to air again. The beam strikes the glass at a 35.0° incident angle. (a) At what angles do the two colors emerge from the glass? red: 35° blue: 35° (b) By what distance (in cm) are the red and blue separated when they emerge?
Answer
Refraction and Separation of Red and Blue Light in a Glass Slab
Problem Setup
- Incident Angle (θ₁): 35.0°
- Glass Thickness (t): 1.80 cm
- Refractive Index of Air (n₁): 1.000
- Red Light Refractive Index (n_red): 1.512
- Blue Light Refractive Index (n_blue): 1.523
Step 1: Refraction Inside the Glass
Snell’s Law: n₁ × sin(θ₁) = n₂ × sin(θ₂)
Red Light:
θ₂_red ≈ 22.3°
Blue Light:
θ₂_blue ≈ 22.12°
Emergent Angle for Both: 35.0° (same as incident angle)
Step 2: Lateral Separation Calculation
s = t × sin(θ₁ − θ₂) / cos(θ₂)
Red Light: s ≈ 0.428 cm
Blue Light: s ≈ 0.433 cm
Separation Distance: |0.433 – 0.428| = 0.00522 cm
Summary Table
| Light Color | Refracted Angle (°) | Emergent Angle (°) | Lateral Shift (cm) |
|---|---|---|---|
| Red | 22.3° | 35.0° | 0.428 |
| Blue | 22.12° | 35.0° | 0.433 |
Total Lateral Separation: 0.00522 cm