Snell's Law Calculator
See how light bends. Calculate the angle of refraction when light passes from air into water, glass, or any other material.
n₁ × sin(θ₁) = n₂ × sin(θ₂)
About Snell's Law:
Snell's Law describes how light bends when passing between media with different refractive indices. When light enters a denser medium, it bends toward the normal. Total internal reflection occurs when light tries to exit a denser medium at a steep angle.
How the Snell's Law Calculator Works
Select what you want to calculate: angle of refraction, angle of incidence, or refractive index of either medium. Enter the known values for the incident medium (n₁), refracting medium (n₂), and the known angle.
The calculator applies Snell's Law: n₁ × sin(θ₁) = n₂ × sin(θ₂). This relates the angles and refractive indices when light crosses a boundary between two materials. The calculator rearranges to solve for your unknown.
Results show the calculated angle or index with proper units. A ray diagram illustrates the light path, showing incident ray, normal line, and refracted ray. Critical angle for total internal reflection is also calculated when applicable.
When You'd Actually Use This
Lens design and analysis
Calculate how light bends at lens surfaces. Essential for designing eyeglasses, camera lenses, microscopes, and telescopes.
Fiber optic communications
Understand total internal reflection in optical fibers. Light stays trapped in the core when incident angle exceeds critical angle.
Underwater vision correction
Calculate why objects look different underwater. Water's refractive index changes how light enters your eye, blurring vision without a mask.
Prism dispersion calculations
Analyze how prisms separate white light into colors. Different wavelengths refract at slightly different angles, creating rainbows.
Gemstone optics
Understand diamond brilliance. High refractive index and precise cutting angles maximize internal reflection and light return.
Atmospheric refraction
Calculate why the sun appears above the horizon after sunset. Air density gradients bend light, extending daylight by several minutes.
What to Know Before Using
Angles are measured from the normal.The normal is perpendicular to the surface, not the surface itself. This is a common source of errors in manual calculations.
Light bends toward normal in denser media.When entering a higher-n material, light slows and bends toward the normal. Exiting to lower-n, it speeds up and bends away.
Total internal reflection has conditions.Occurs only when going from higher to lower index, and angle exceeds critical angle. Critical angle: θc = arcsin(n₂/n₁).
Refractive index depends on wavelength.Blue light refracts more than red (dispersion). This is why prisms create rainbows and lenses have chromatic aberration.
Pro tip: When light enters perpendicular to the surface (angle = 0°), there's no bending regardless of refractive indices. The ray continues straight, just at a different speed.
Common Questions
What is refractive index?
n = c/v, the ratio of light speed in vacuum to speed in the material. Vacuum n=1, air ≈1.0003, water ≈1.33, glass ≈1.5, diamond ≈2.42.
Why does light bend at boundaries?
Light changes speed in different materials. If it hits at an angle, one side of the wavefront slows first, causing the wave to turn.
Can refractive index be less than 1?
Not for normal materials. Phase velocity can exceed c in some cases, but information still travels at or below c. Metamaterials can have negative n.
What happens at the critical angle?
Refracted ray travels along the boundary (90° from normal). Beyond critical angle, all light reflects internally - no transmission.
Does Snell's Law work for sound?
Yes, any wave phenomenon follows Snell's Law. Sound waves refract at boundaries between materials with different sound speeds.
Why do pools look shallower than they are?
Light from the bottom bends away from normal exiting water. Your brain traces rays back straight, making the bottom appear closer than it is.
What's the maximum refraction angle?
For light entering from air, maximum refraction is the critical angle (about 49° for water, 42° for typical glass). Beyond that, total internal reflection occurs.
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