Snell's Law
Refraction of light between two media.
Formula
Variables
How it works
Snell's law links how much a light ray bends when it crosses from one material into another. The refractive index tells you how strongly a medium slows light compared with vacuum, and the change in speed across the boundary forces the ray to change direction so that the ratio of the sines of the angles matches the ratio of refractive indices. This relationship comes from the wave nature of light and the requirement that the wavefront stays continuous at the interface.
When to use it
Use this formula whenever a light ray passes between two transparent media, such as air to glass, water to acrylic, or glass to water. It is the standard tool for finding an unknown angle of refraction or an unknown refractive index in lens, prism, and fiber-optics problems.
Worked example, step by step
A laser beam in air strikes a block of glass at an angle of 40° to the normal. The refractive index of air is 1.00 and the refractive index of the glass is 1.50. Step 1: Write Snell's law: n1 sin(θ1) = n2 sin(θ2) Step 2: Substitute the known values: 1.00 × sin(40°) = 1.50 × sin(θ2) Step 3: Calculate sin(40°): 0.643 Step 4: Solve for sin(θ2): sin(θ2) = 0.643 / 1.50 = 0.429 Step 5: Take the inverse sine: θ2 = sin^-1(0.429) ≈ 25.4° Final answer: the refracted angle in the glass is about 25.4°
Common mistakes to avoid
- measuring the angle from the surface instead of from the normal
- swapping n1 and n2 when setting up the equation
- using degrees in some steps and radians in others on the calculator
Did You Know?
Snell's law bends light at boundaries and is why a straw looks broken where it enters a glass of water.
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