Interactive Index of Refraction Calculator
How to Use This Calculator
This calculator determines various optical properties based on the index of refraction and Snell's Law.
- Select which variable you want to calculate from the dropdown menu.
- Enter the required known values in the input fields that appear. Angles should be in degrees.
- The speed of light in vacuum (c) is taken as approximately 299,792,458 m/s.
- Click the "Calculate" button.
- Results, including a step-by-step solution, will be displayed.
Theory: Index of Refraction & Snell's Law
The index of refraction (or refractive index) of a material, denoted by 'n', is a dimensionless number that describes how fast light travels through that material. It is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v):
n = c / v
A higher refractive index means light travels slower in that medium. Since light travels fastest in a vacuum, the refractive index of any medium is always greater than or equal to 1 (n ≥ 1).
Snell's Law (also known as the law of refraction) describes the relationship between the angles of incidence and refraction and the refractive indices of two media when light passes from one medium to another. It is given by:
n1 sin(θ1) = n2 sin(θ2)
Where n1 and θ1 are the refractive index and angle of incidence in the first medium, and n2 and θ2 are for the second medium. Angles are measured with respect to the normal (a line perpendicular to the surface).
If light enters a medium with a higher refractive index (n2 > n1), it bends towards the normal (θ2 < θ1). If it enters a medium with a lower refractive index (n2 < n1), it bends away from the normal.
Total Internal Reflection (TIR): When light travels from a denser medium (higher n) to a less dense medium (lower n), if the angle of incidence exceeds a certain critical angle (θc), all the light is reflected back into the first medium. This calculator will note if conditions for TIR might be met or if a calculated sine value is greater than 1.
Formulas Used
Speed of Light in Vacuum (c) ≈ 2.99792458 × 108 m/s
- 1. Refractive Index (n) from speed (v):
n = c / v - 2. Speed of Light in Medium (v) from n:
v = c / n - 3. Snell's Law:
n1 sin(θ1) = n2 sin(θ2)- For n1:
n1 = (n2 sin(θ2)) / sin(θ1) - For n2:
n2 = (n1 sin(θ1)) / sin(θ2) - For θ1:
θ1 = arcsin((n2 sin(θ2)) / n1) - For θ2:
θ2 = arcsin((n1 sin(θ1)) / n2)
- For n1:
Refractive Index Properties Calculation
Speed of Light in Vacuum (c) ≈ 2.9979 × 108 m/s