HesapHanem

Total Internal Reflection Angle Calculator

Enter the refractive indices of the two media to find the critical angle.

How it is calculated

The critical angle follows from Snell's law when the refracted ray would just graze the boundary, at 90°: θc = arcsin(n₂ / n₁). Here n₁ is the refractive index of the medium the light starts in and n₂ is that of the medium it would enter. Both are unitless numbers. The engine computes the ratio, takes the arcsine in radians and also converts it to degrees. Both must be positive (zero or below returns no result), and n₂ may not exceed n₁: if light goes into a denser medium there is no critical angle, and the tool returns no result. Degrees are rounded to two decimals and radians to four. For any angle of incidence larger than θc, measured from the normal, all of the light is reflected.

Worked example

Light travels inside glass with refractive index 1.5 toward the boundary with air, index 1. The ratio is n₂ / n₁ = 1 / 1.5 = 0.6667. The arcsine of 0.6667 is 0.7297 rad, and multiplying by 180 / π gives 41.81°. Any ray inside the glass that meets the surface at more than 41.81° from the normal is totally reflected, while rays below that angle partly escape into the air.

Try this example →

Common mistakes

  • Swapping the two indices. n₁ must be the denser medium where the light starts, so glass to air is 1.5 and 1, not 1 and 1.5; the reverse order returns no result because no critical angle exists going into glass.
  • Measuring the angle from the surface instead of from the normal. The critical angle is measured from the perpendicular, so a ray at 41.81° to the normal is at 48.19° to the surface.
  • Expecting the angle to depend on wavelength or thickness. The tool uses one index per medium, but real glass has a slightly different index for each colour, so the angle shifts a little.
  • Entering equal indices and trusting the 90.00° result. When n₁ = n₂ there is no boundary effect at all, and total reflection never occurs.
  • Using a speed of light or a density instead of a refractive index. Both fields expect the dimensionless ratio of the speed of light in vacuum to its speed in the medium, such as 1.33 for water.

About this calculator

Total internal reflection occurs when light traveling from a denser medium into a less dense one strikes the boundary at an angle of incidence (measured from the normal) larger than a threshold called the critical angle, at which point all the light reflects back instead of refracting through. The critical angle is found with θc = arcsin(n₂ ÷ n₁), where n₁ is the refractive index of the denser medium the light starts in and n₂ is the refractive index of the medium it would otherwise enter — this only has a solution when n₁ is greater than n₂.

Optical and fiber-optic engineers rely on total internal reflection to keep light confined inside a fiber core as it travels long distances with minimal loss, which is why the critical angle between the core and cladding materials is a key design parameter. The same principle explains everyday optical effects — like the shimmering underwater "mirror" seen when looking up at a shallow, grazing angle toward a water surface, or how prisms and binoculars redirect light without a reflective coating.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    A glass-to-air boundary with an index of 1.5 gives a critical angle of 41.81 degrees, while water at 1.33 gives 48.75 degrees. The angle is measured from the normal: a ray meeting the surface at a smaller angle partly escapes, and a larger one is fully reflected. This only exists when light goes from a higher index to a lower one. Which pair of materials are you checking, say for a fibre or a prism?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators