Snell's Law
Light bends when passing between media of different refractive index.
Formula
Variables
Example
A straw in a glass of water looks bent because light refracts at the surface.
How it works
Snell’s law tells you how much a light ray changes direction when it crosses from one material into another, such as air to glass or water to air. The refractive index measures how strongly a material slows light compared with vacuum, and the sine relationship comes from the wave nature of light and the requirement that the wavefront stays continuous at the boundary. In general, light bends toward the normal when it enters a higher refractive index medium and away from the normal when it enters a lower one.
When to use it
Use this formula whenever you need to find an unknown angle of refraction, determine a refractive index, or analyze how light travels through lenses, prisms, fibers, or transparent materials. It is especially useful in optics problems involving air-water, air-glass, or glass-plastic boundaries.
Worked example, step by step
A beam of light in air ( n_1 = 1.00) strikes a glass surface ( n_2 = 1.50) at an incident angle of 30 0 to the normal. Use Snell's law: n_1 sinf1_1 = n_2 sinf1_2 Substitute values: 1.00 b7 sin(30 0) = 1.50 b7 sin(f1_2) Compute sin(30 0) = 0.5, so 0.5 = 1.50 b7 sin(f1_2) Divide by 1.50: sin(f1_2) = 0.5 / 1.50 = 0.333... Take the inverse sine: f1_2 = sin07B1(0.333...) e 19.5 0 Final answer: the refracted ray enters the glass at about 19.5 0 to the normal.
Common mistakes to avoid
- measuring the angle from the surface instead of from the normal
- swapping n1 and n2, which reverses the bending direction
- forgetting that the sine function, not the angle itself, is what must match across the boundary
Did You Know?
Snell's law governs everything from eyeglasses to fiber-optic cables carrying the internet.
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