Snell's law of refraction

Snell's Law describes how light bends when passing between media:

We'll visualize this using the ratio and animate the incident angle.

Setup

Define the refractive index ratio and fixed height:

• Refractive index ratio
• Height y = 3
• Incident angle (degrees) = 30

Convert angle to radians:

• Convert to radians

Draw the interface and normal:

• Interface left
• Interface right
• Draw interface
• Normal top
• Normal bottom
• Draw normal
• Hide unnecessary points

Set line colors to be different:

• Define color
• Set color of first line
• Set color of second line

Calculate incident ray start point: (-y tan θ₁, y)

• Calculate
• Calculate
• Negate for x coordinate
• Start point

Calculate refraction angle using Snell's Law:

• Calculate
• Calculate
• Calculate
• Calculate in degrees

Calculate refracted ray end point: (y tan \theta_2, -y)

• Calculate
• Calculate
• Negate y
• End point

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Draw the light rays:

• Draw incident ray
• Draw refracted ray
• Calculate wrt x-axis and draw arc for theta1
• Calculate wrt x-axis and draw arc for theta2

Highlight the two rays:

• Incident ray and angle
• Refracted ray and angle

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Experiment with different scenarios

Case 1: Light entering denser medium (n₁/n₂ < 1)

• Start with zero degrees (vertical rays)
• Animate the angle to 90°

Notice how the refracted ray bends toward the normal.

Case 2: Light entering less dense medium (n₁/n₂ > 1)

• Reset angle to 10°
• Switch to glass-to-air (n₁/n₂ = 1.5)
• Animate to 40°

Notice how the refracted ray bends away from the normal.

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The Critical Angle

When , there exists a critical angle θc beyond which refraction cannot occur. At the critical angle, the refracted ray travels along the interface (θ₂ = 90°).

Calculate critical angle

• Calculate
• Critical angle (radians)
• Critical angle (degrees)

Highlight the critical angle - For glass to air (n₁/n₂ = 1.5), ≈ 41.8°.

Try angles approaching the critical angle:

• 10° below critical
• 5° below critical
• 1° below critical
• At critical angle

At the critical angle, the refracted ray becomes parallel to the interface. Beyond this angle, total internal reflection occurs (not shown here).

Try other material combinations:

• Water to air (1.33) - θc ≈ 48.6°
• Diamond to air (2.42) - θc ≈ 24.4°