Snell's Law
Refraction of light between two media.
Formula
Variables
Example
Light from air (n=1) into water (n=1.33) at 30° bends to θ ≈ 22°.
How it works
Snell's Law tells you how a light ray changes direction when it crosses from one medium into another because its speed changes at the boundary. The refractive index measures how much a medium slows light down, and the sine relationship comes from requiring the wavefronts to stay continuous across the interface, which preserves phase along the boundary. If the second medium has a higher refractive index, the ray bends toward the normal; if it has a lower refractive index, it bends away from the normal.
When to use it
Use this whenever you need the angle of refraction, the unknown refractive index, or to analyze bending of rays at material boundaries such as air-glass, water-air, fiber optics, lenses, or atmospheric layers. It is also the starting point for advanced optics problems involving critical angle and total internal reflection.
Worked example, step by step
A laser beam travels from crown glass into water. The glass has refractive index n1 = 1.52, the water has n2 = 1.33, and the incident angle in the glass is θ1 = 40°. Step 1: Write Snell's Law: n1 sin θ1 = n2 sin θ2 Step 2: Substitute the values: 1.52 sin(40°) = 1.33 sin(θ2) Step 3: Compute the left side: 1.52 × 0.6428 ≈ 0.977 Step 4: Solve for sin(θ2): sin(θ2) = 0.977 / 1.33 ≈ 0.735 Step 5: Take the inverse sine: θ2 = sin^-1(0.735) ≈ 47.3° Final answer: the refracted angle in water is about 47°.
Common mistakes to avoid
- mixing up the incident angle and refracted angle on the wrong side of the equation
- measuring angles from the surface instead of from the normal
- forgetting that refractive indices and angles must be used consistently for the same wavelength and medium pair
Did You Know?
Snell's law explains why a straw looks bent in a glass of water — light changes speed as it enters.
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