Angle of incidence (°) Enter the angle in degrees (0 to 90)

Refractive index of medium 1 (n1) Enter index for the starting material (e.g., air is ~1.00)

Refractive index of medium 2 (n2) Enter index for the second material (e.g., water is ~1.33)

Quick Examples:

Air to Water Glass to Air

Calculate Clear

This calculator is for informational purposes only. It provides estimates based on standard optical formulas. Verify results with appropriate professionals for important applications.

What Is Refracted Angle

The refracted angle is the angle at which a light ray travels after it passes from one material into another. When light moves between materials like air, water, or glass, it changes speed. This change in speed causes the light to bend, or refract. The refracted angle measures this new direction relative to a vertical line known as the normal.

How Refracted Angle Is Calculated

Formula

This formula compares how fast light moves in two different materials. First, we multiply the index of the first material by the sine of the incoming angle. This gives us a value that must stay constant. To find the new angle, we divide this constant by the index of the second material. We then use the inverse sine function to find the angle that produces that value.

Why Refracted Angle Matters

Knowing how light bends is important for designing lenses, glasses, and cameras. It helps us predict where light will go after it hits a surface. This allows us to create tools that focus light correctly to improve vision or capture images.

Why Understanding Light Bending Is Important for Design

If designers ignore how light refracts, lenses may not focus images clearly. This can cause blurry vision in eyeglasses or poor quality in optical instruments. Understanding this concept helps in making precise corrections to ensure light lands exactly where it is needed for clear vision.

For Total Internal Reflection

In some cases, light cannot pass into the second material and is instead reflected back entirely. This happens when light moves from a dense material to a less dense one at a steep angle. Calculating this helps engineers design fiber optic cables that carry data over long distances without losing signal strength.