Optics & beams

Refractive index, group index and material dispersion of fused silica, N-BK7, N-SF11, calcium fluoride, sapphire and silicon from published Sellmeier equations, or from your own coefficients, with the Abbe number, zero-dispersion wavelength, plots, guided experiments and a validation table.

Near and far limits of sharpness, hyperfocal distance and the diffraction limit for a camera lens, and the depth of field of a microscope objective from its NA, magnification and camera pixel size, with plots, presets, guided experiments and a validation table.

Image distance, magnification, image height and image type from the thin lens equation for converging and diverging lenses, or a pair of lenses with its effective focal length, with a live ray diagram, presets from a magnifier to a microscope, guided experiments and a validation table.

Refracted angle, critical angle and Brewster angle for any two refractive indices, with Fresnel reflectance and transmittance for s, p and unpolarized light and the evanescent depth under total internal reflection, with a ray diagram, reflectance curves, presets, guided experiments and a validation table.

Complex Fresnel reflection coefficients for s and p polarization at any angle, the reflectance and its phase, the phase difference and ellipsometric angles, the Brewster, pseudo-Brewster and critical angles, and absorbing media with a complex refractive index, with reflectance and phase plots, presets, guided experiments and a validation table.

The 1/e² beam radius, diameter and FWHM from the blade travel between two power levels of a knife-edge scan, or from a least-squares error-function fit to the pasted scan with its center, background and residual, with a fit plot, presets, guided experiments and a validation table.

The focused spot diameter of a laser beam from its wavelength, diameter at the lens, focal length and M², with the exact Gaussian lens transformation, the Rayleigh range and depth of focus, the convergence angle, the peak intensity and the power clipped by the lens aperture, with plots, presets, guided experiments and a validation table.

The color of monochromatic light from its wavelength: the color name, the nearest sRGB color as a hex code by clipping or by adding white, the CIE 1931 chromaticity and tristimulus values, the photopic and scotopic luminous efficiency and the photon energy, with a spectrum plot, a chromaticity diagram, presets, guided experiments and a validation table.

The Abbe number Vd from three refractive indices or from the Sellmeier coefficients of common optical materials, with Ve, the partial dispersion, the crown or flint family, the chromatic focal shift of a singlet and the element focal lengths of a thin achromatic doublet, with a glass map, presets, guided experiments and a validation table.

The critical angle for total internal reflection from two refractive indices, the escape cone of an emitter, and beyond the critical angle the evanescent penetration depth of the field and intensity and the phase shifts of s and p light, with plots, presets, guided experiments and a validation table.