Angle of Incidence Calculator
Calculate the angle of incidence using Snell's Law given refractive indices and angle of refraction. Includes Fresnel reflectance and Brewster angle.
Calculate laser radiance (brightness), spectral radiance, intensity, beam parameter product, and M² factor. Supports CW and pulsed modes.
| Light Source | Brightness (W/m²·sr) |
|---|---|
| Sun (surface) | 2.0e7 |
| LED (high-power) | 1.0e7 |
| He-Ne laser (1 mW) | 1.5e9 |
| Fiber laser (10 W) | ~1e12 |
| Industrial CO₂ (1 kW) | ~1e10 |
| Your laser | 6.48e+11 |
Laser brightness — technically called radiance — is the most comprehensive figure of merit for a laser source. Defined as power per unit area per unit solid angle (W/m²·sr), radiance captures both the spatial concentration and directionality of the beam in a single number. Unlike raw power, which says nothing about beam quality, radiance tells you how effectively the light can be focused or projected.
A milliwatt He-Ne laser can have higher radiance than the surface of the Sun because its beam is extraordinarily well collimated and concentrated. Industrial fiber lasers achieve radiance values of 10¹² W/m²·sr or more, enabling precise material processing, long-range LIDAR, and free-space optical communication. For pulsed lasers, peak brightness during each pulse can be many orders of magnitude higher than the average brightness.
This calculator computes both CW and pulsed laser brightness from beam parameters (power, diameter, divergence), along with spectral radiance, irradiance, beam parameter product (BPP), and M² beam quality factor. A comparison table puts your laser in context alongside common light sources from LEDs to ultrafast lasers, and a logarithmic brightness scale provides visual perspective.
This calculator improves speed and consistency while reducing avoidable mistakes in practical workflows.
Radiance B = P / (A · Ω), where A = π(d/2)² and Ω = π(θ/2)². BPP = w₀ × θ_half. M² = BPP / (λ/π). Peak power = E / τ for pulsed lasers.Result: 1.02 × 10¹² W/(m²·sr)
A 10 W fiber laser with 5 mm beam and 0.5 mrad divergence: area = π(2.5e-3)² ≈ 1.96e-5 m², solid angle = π(0.25e-3)² ≈ 1.96e-7 sr. B = 10 / (1.96e-5 × 1.96e-7) ≈ 2.6e12 W/(m²·sr).
Calculate laser radiance (brightness), spectral radiance, intensity, beam parameter product, and M² factor. Supports CW and pulsed modes. Use it when you need a repeatable calculation in the physics / optics category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.
Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.
Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.
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Power alone doesn't indicate how concentrated the light is. A 100 W lightbulb is much less bright than a 1 W laser because the laser's energy is confined to a tiny solid angle.
BPP (mm·mrad) is the product of beam waist radius and half-angle divergence. Lower BPP means higher beam quality. The diffraction limit is λ/π.
Yes, easily. Even a milliwatt laser pointer has higher radiance than the Sun because the Sun radiates into 4π steradians while the laser emits into microsteradians.
During each pulse, the instantaneous power can be millions of times higher than the average, producing correspondingly higher peak brightness.
M² (M-squared) compares the beam's BPP to the diffraction limit. M²=1 is ideal Gaussian. Multimode lasers may have M²=10-100.
Improve beam quality (lower M²), increase power, or use a beam expander (reduces divergence while conserving brightness for ideal beams).
Calculate the angle of incidence using Snell's Law given refractive indices and angle of refraction. Includes Fresnel reflectance and Brewster angle.
Calculate the angle of refraction using Snell's Law. Includes critical angle, Brewster angle, Fresnel reflectance, and a multi-angle comparison table.
Calculate angular resolution using the Rayleigh criterion, Dawes' limit, and Sparrow limit. Compare apertures and find minimum resolvable features.