Snell's Law of Refraction Lab

PrayogSetu • Optical Refraction & Total Internal Reflection Simulator

Optical Refraction Bench

MEDIUM 1: AIR (n₁ = 1.00)
MEDIUM 2: GLASS (n₂ = 1.50)

Live Optical Measurements

Real-time Data
Incident Angle (θ₁) 45.0°
Refracted Angle (θ₂) 28.1°
Refractive Index 1 (n₁) 1.00
Refractive Index 2 (n₂) 1.50
Speed in Medium 1 (v₁) 3.00 × 10⁸ m/s
Speed in Medium 2 (v₂) 2.00 × 10⁸ m/s

Bending Analysis & Critical Angle

↘
BENDS TOWARD NORMAL Ray slows down upon entering Medium 2
θ₁ (Incident): 45.0°
θ₂ (Refracted): 28.1°
Deviation (|θ₁ - θ₂|): 16.9°

Light Speed in Media Visualization

v = c / n
MEDIUM 1 (AIR, n₁=1.00) 3.00 × 10⁸ m/s (100% c)
MEDIUM 2 (GLASS, n₂=1.50) 2.00 × 10⁸ m/s (67% c)

Refraction Graph (θ₂ vs θ₁)

Snell's Law Curve

Theoretical Curve     Current Angle     Critical Angle

Snell's Law Real-time Verification

n₁ sin(θ₁) = n₂ sin(θ₂)
INCIDENT SIDE
n₁ × sin(θ₁)
1.00 × sin(45.0°)
0.7071
=
REFRACTED SIDE
n₂ × sin(θ₂)
1.50 × sin(28.1°)
0.7071
Absolute Deviation Error: 0.0000
✓ SNELL'S LAW VERIFIED

Experimental Observation Table

Logged Data Points
Trial Medium 1 n₁ Medium 2 n₂ Incident Angle (θ₁) Refracted Angle (θ₂) Critical Angle (θc) Result / Phenomenon
No experimental readings logged yet. Click "Add Current Reading" above to record observations.

Guided Laboratory Procedure

Step-by-Step
  1. Select Medium 1: Choose the incident optical medium from the presets (e.g. Air n = 1.00) or adjust the n₁ slider.
  2. Select Medium 2: Choose the second optical medium (e.g. Glass n = 1.50) or adjust the n₂ slider.
  3. Set Angle of Incidence: Drag the θ₁ slider to set an initial incident angle (e.g., 45.0°).
  4. Observe Incident Ray: Trace the incoming light beam traveling through Medium 1 toward the interface.
  5. Observe Normal Line: Locate the vertical perpendicular normal line dashed at the point of incidence.
  6. Observe Refracted Ray: Note how the ray bends at the boundary upon entering Medium 2.
  7. Record Angle of Refraction: Read the calculated angle θ₂ from the arc label or measurements panel.
  8. Vary Angle of Incidence: Move θ₁ from 0° to 89° and observe the shift in θ₂.
  9. Vary Medium 2: Change Medium 2 to Water (n = 1.33) or Diamond (n = 2.42) and compare the bending magnitude.
  10. Compare Bending Direction: Note that entering a higher index medium (n₂ > n₁) bends light toward the normal, while entering a lower index medium (n₂ < n₁) bends light away from the normal.
  11. Find Critical Angle: Set n₁ > n₂ (e.g. Glass to Air). Gradually increase θ₁ until θ₂ reaches 90.0°.
  12. Observe Total Internal Reflection: Increase θ₁ beyond the critical angle (θ₁ > θ_c) to witness Total Internal Reflection (TIR), where light is 100% reflected back into Medium 1.
  13. Record Observations & Verify: Click "Add Current Reading" to log trials and check the Snell's Law verification panel.

About Snell's Law of Refraction

Physics Theory

1. Snell's Law Equation

\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]

Where \(n_1\) and \(n_2\) are the dimensionless refractive indices of Medium 1 and Medium 2, \(\theta_1\) is the angle of incidence, and \(\theta_2\) is the angle of refraction measured relative to the normal line.

2. Refractive Index & Speed of Light

The refractive index \(n\) of an optical medium is defined as the ratio of light speed in vacuum (\(c \approx 3.00 \times 10^8 \text{ m/s}\)) to light speed in the medium (\(v\)):

\[ n = \frac{c}{v} \implies v = \frac{c}{n} \]

When light crosses a boundary into an optically denser medium (\(n_2 > n_1\)), its phase velocity decreases, causing the wavefronts to tilt and bend toward the normal.

3. Critical Angle & Total Internal Reflection (TIR)

When light travels from an optically denser medium into a rarer medium (\(n_1 > n_2\)), the refracted ray bends away from the normal (\(\theta_2 > \theta_1\)). The incident angle at which \(\theta_2 = 90^\circ\) is the Critical Angle (\(\theta_c\)):

\[ \sin(\theta_c) = \frac{n_2}{n_1} \implies \theta_c = \arcsin\left(\frac{n_2}{n_1}\right) \]

For incident angles greater than \(\theta_c\) (\(\theta_1 > \theta_c\)), no light passes into Medium 2. All light is entirely reflected back into Medium 1, a phenomenon known as Total Internal Reflection (TIR).