Calculator
Example Data Table
| Example | Given | Computed n (approx.) | Notes |
|---|---|---|---|
| Snell’s law | n₁=1.000, θᵢ=45°, θᵣ=28° | 1.513 | Typical for many crown glasses. |
| Critical angle | n₂=1.000, θc=42° | 1.494 | Common around visible wavelengths. |
| Speed method | v=2.00×10⁸ m/s | 1.499 | Uses c/v with c=299,792,458 m/s. |
| Wavelength ratio | λ₀=589 nm, λm=388 nm | 1.518 | Frequency unchanged at boundary. |
| Apparent depth | Real=10 mm, Apparent=6.7 mm | 1.493 | Best near-normal viewing angles. |
| Prism deviation | A=60°, Dmin=37° | 1.517 | Classic lab method at fixed wavelength. |
Formula Used
- Snell’s law: n₁·sin(θᵢ) = n_glass·sin(θᵣ) → n_glass = n₁·sin(θᵢ)/sin(θᵣ)
- Critical angle: sin(θc) = n₂/n_glass → n_glass = n₂/sin(θc)
- Speed relation: n_glass = c/v, where c = 299,792,458 m/s
- Wavelength ratio: n_glass = λ₀/λm (same units)
- Apparent depth: n_glass = real depth / apparent depth
- Prism minimum deviation: n_glass = sin((A + Dmin)/2) / sin(A/2)
How to Use This Calculator
- Select the measurement method that matches your setup.
- Enter your values carefully, using degrees for angles.
- Choose the decimal places for your preferred precision.
- Press Calculate to see the result above the form.
- Use the CSV or PDF buttons to export the displayed result.
Article: Glass Refractive Index Explained
1) What the refractive index means
The refractive index (n) compares light speed in vacuum to light speed in glass. If n = 1.50, light travels at about 299,792,458 / 1.50 ≈ 199,861,639 m/s inside that glass. This value helps predict bending at surfaces.
2) Typical glass index values
Common materials cluster in predictable ranges. Fused silica is about 1.458, borosilicate about 1.474, and many crown or soda‑lime glasses are near 1.50–1.52. Dense flint glasses can be around 1.60–1.70, depending on composition.
For quick checks, treat 1.50–1.52 as “typical clear glass.” Optical catalogs may list n at a standard line (often 589 nm) and a matching Abbe number for dispersion.
3) Wavelength and dispersion
Glass is dispersive, so n changes with wavelength. Shorter wavelengths (blue) usually see a slightly higher n than longer wavelengths (red). Even a small change, such as 0.005–0.020 across the visible band, can affect prism separation and lens chromatic aberration.
As a rough example, a glass with n = 1.517 at 589 nm might read closer to 1.522 near 486 nm and nearer 1.514 around 656 nm. Your measured wavelength matters.
4) Using Snell’s law angle data
With Snell’s law, you enter n₁, θᵢ, and θᵣ to compute n. For example, n₁ = 1.000, θᵢ = 45°, and θᵣ = 28° gives n ≈ 1.513. Better angle resolution (±0.2°) can noticeably reduce uncertainty.
If your incident medium is air, using n₁ = 1.0003 instead of 1.0000 can slightly shift the result. Keep angles in degrees and measure from the normal to the surface.
5) Critical angle measurements
If light goes from glass to air, total internal reflection begins beyond the critical angle θc. Using n = n₂ / sin(θc), air (n₂ ≈ 1.000) and θc = 42° yields n ≈ 1.494. Ensure you are measuring the onset point, not a brighter reflection.
6) Prism minimum deviation method
In many labs, a prism is rotated until deviation is minimum (Dmin). With apex angle A = 60° and Dmin = 37°, the calculator gives n ≈ 1.517. This method is stable because the light path is symmetric at minimum deviation.
7) Apparent depth ratio data
For near‑normal viewing, n ≈ real depth / apparent depth. A 10 mm real depth that appears as 6.7 mm gives n ≈ 1.493. Keep viewing close to perpendicular; oblique viewing makes the simple ratio less accurate.
8) Where these numbers matter
Refractive index guides lens design, coatings, fiber‑optic acceptance angles, and even smartphone camera stacks. Small index shifts can change focal length, reflection losses, and critical angle behavior. Use this calculator to verify measurements and compare them to reference glass types.
Index also controls surface reflections. At normal incidence, reflectance is about R = ((n−1)/(n+1))². For n = 1.50, R ≈ 4% per air‑glass surface, motivating anti‑reflection coatings.
FAQs
1) What does refractive index tell me?
It shows how much glass slows light compared to vacuum. Higher n generally means stronger bending at a surface and a lower light speed inside the glass.
2) What is a common refractive index for window glass?
Many soda‑lime window glasses are around 1.50 to 1.52 near visible light. Exact values vary with composition and the wavelength used.
3) Why do results depend on wavelength?
Glass is dispersive, so n changes with color. Blue light often has a slightly higher n than red light, which is why prisms spread white light into a spectrum.
4) Which method should I choose?
Use Snell’s law if you can measure incident and refracted angles. Use critical angle for total internal reflection setups. Use prism minimum deviation for classic lab prisms.
5) What if my computed n is below 1.0?
That usually indicates a measurement or unit error. Recheck angles, ensure degrees are used, and confirm you entered the correct “incident” and “refracted” angles.
6) Can temperature change the refractive index?
Yes, n can shift slightly with temperature. The change is often small for many glasses, but precision work should control temperature or record it with the measurement.
7) Does this calculator give a “true” constant for glass?
It gives an estimate based on your inputs and method. The value depends on wavelength, glass type, and measurement accuracy, so treat it as condition‑specific.